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Deductive Reasoning

- Calculus
- Absolute Maxima and Minima
- Absolute and Conditional Convergence
- Accumulation Function
- Accumulation Problems
- Algebraic Functions
- Alternating Series
- Antiderivatives
- Application of Derivatives
- Approximating Areas
- Arc Length of a Curve
- Area Between Two Curves
- Arithmetic Series
- Average Value of a Function
- Calculus of Parametric Curves
- Candidate Test
- Combining Differentiation Rules
- Combining Functions
- Continuity
- Continuity Over an Interval
- Convergence Tests
- Cost and Revenue
- Density and Center of Mass
- Derivative Functions
- Derivative of Exponential Function
- Derivative of Inverse Function
- Derivative of Logarithmic Functions
- Derivative of Trigonometric Functions
- Derivatives
- Derivatives and Continuity
- Derivatives and the Shape of a Graph
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Polar Functions
- Derivatives of Sec, Csc and Cot
- Derivatives of Sin, Cos and Tan
- Determining Volumes by Slicing
- Direction Fields
- Disk Method
- Divergence Test
- Eliminating the Parameter
- Euler's Method
- Evaluating a Definite Integral
- Evaluation Theorem
- Exponential Functions
- Finding Limits
- Finding Limits of Specific Functions
- First Derivative Test
- Function Transformations
- General Solution of Differential Equation
- Geometric Series
- Growth Rate of Functions
- Higher-Order Derivatives
- Hydrostatic Pressure
- Hyperbolic Functions
- Implicit Differentiation Tangent Line
- Implicit Relations
- Improper Integrals
- Indefinite Integral
- Indeterminate Forms
- Initial Value Problem Differential Equations
- Integral Test
- Integrals of Exponential Functions
- Integrals of Motion
- Integrating Even and Odd Functions
- Integration Formula
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- Integration Using Long Division
- Integration of Logarithmic Functions
- Integration using Inverse Trigonometric Functions
- Intermediate Value Theorem
- Inverse Trigonometric Functions
- Jump Discontinuity
- Lagrange Error Bound
- Limit Laws
- Limit of Vector Valued Function
- Limit of a Sequence
- Limits
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- Limits of a Function
- Linear Approximations and Differentials
- Linear Differential Equation
- Linear Functions
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- Logarithmic Functions
- Logistic Differential Equation
- Maclaurin Series
- Manipulating Functions
- Maxima and Minima
- Maxima and Minima Problems
- Mean Value Theorem for Integrals
- Models for Population Growth
- Motion Along a Line
- Motion in Space
- Natural Logarithmic Function
- Net Change Theorem
- Newton's Method
- Nonhomogeneous Differential Equation
- One-Sided Limits
- Optimization Problems
- P Series
- Particle Model Motion
- Particular Solutions to Differential Equations
- Polar Coordinates
- Polar Coordinates Functions
- Polar Curves
- Population Change
- Power Series
- Radius of Convergence
- Ratio Test
- Removable Discontinuity
- Riemann Sum
- Rolle's Theorem
- Root Test
- Second Derivative Test
- Separable Equations
- Separation of Variables
- Simpson's Rule
- Solid of Revolution
- Solutions to Differential Equations
- Surface Area of Revolution
- Symmetry of Functions
- Tangent Lines
- Taylor Polynomials
- Taylor Series
- Techniques of Integration
- The Fundamental Theorem of Calculus
- The Mean Value Theorem
- The Power Rule
- The Squeeze Theorem
- The Trapezoidal Rule
- Theorems of Continuity
- Trigonometric Substitution
- Vector Valued Function
- Vectors in Calculus
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- Washer Method
- Decision Maths
- Geometry
- 2 Dimensional Figures
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- 3-Dimensional Figures
- Altitude
- Angles in Circles
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- Area and Volume
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- Area of Parallelograms
- Area of Plane Figures
- Area of Rectangles
- Area of Regular Polygons
- Area of Rhombus
- Area of Trapezoid
- Area of a Kite
- Composition
- Congruence Transformations
- Congruent Triangles
- Convexity in Polygons
- Coordinate Systems
- Dilations
- Distance and Midpoints
- Equation of Circles
- Equilateral Triangles
- Figures
- Fundamentals of Geometry
- Geometric Inequalities
- Geometric Mean
- Geometric Probability
- Glide Reflections
- HL ASA and AAS
- Identity Map
- Inscribed Angles
- Isometry
- Isosceles Triangles
- Law of Cosines
- Law of Sines
- Linear Measure and Precision
- Median
- Parallel Lines Theorem
- Parallelograms
- Perpendicular Bisector
- Plane Geometry
- Polygons
- Projections
- Properties of Chords
- Proportionality Theorems
- Pythagoras Theorem
- Rectangle
- Reflection in Geometry
- Regular Polygon
- Rhombuses
- Right Triangles
- Rotations
- SSS and SAS
- Segment Length
- Similarity
- Similarity Transformations
- Special quadrilaterals
- Squares
- Surface Area of Cone
- Surface Area of Cylinder
- Surface Area of Prism
- Surface Area of Sphere
- Surface Area of a Solid
- Surface of Pyramids
- Symmetry
- Translations
- Trapezoids
- Triangle Inequalities
- Triangles
- Using Similar Polygons
- Vector Addition
- Vector Product
- Volume of Cone
- Volume of Cylinder
- Volume of Pyramid
- Volume of Solid
- Volume of Sphere
- Volume of prisms
- Mechanics Maths
- Acceleration and Time
- Acceleration and Velocity
- Angular Speed
- Assumptions
- Calculus Kinematics
- Coefficient of Friction
- Connected Particles
- Conservation of Mechanical Energy
- Constant Acceleration
- Constant Acceleration Equations
- Converting Units
- Elastic Strings and Springs
- Force as a Vector
- Kinematics
- Newton's First Law
- Newton's Law of Gravitation
- Newton's Second Law
- Newton's Third Law
- Power
- Projectiles
- Pulleys
- Resolving Forces
- Statics and Dynamics
- Tension in Strings
- Variable Acceleration
- Work Done by a Constant Force
- Probability and Statistics
- Bar Graphs
- Basic Probability
- Charts and Diagrams
- Conditional Probabilities
- Continuous and Discrete Data
- Frequency, Frequency Tables and Levels of Measurement
- Independent Events Probability
- Line Graphs
- Mean Median and Mode
- Mutually Exclusive Probabilities
- Probability Rules
- Probability of Combined Events
- Quartiles and Interquartile Range
- Systematic Listing
- Pure Maths
- ASA Theorem
- Absolute Value Equations and Inequalities
- Addition and Subtraction of Rational Expressions
- Addition, Subtraction, Multiplication and Division
- Algebra
- Algebraic Fractions
- Algebraic Notation
- Algebraic Representation
- Analyzing Graphs of Polynomials
- Angle Measure
- Angles
- Angles in Polygons
- Approximation and Estimation
- Area and Circumference of a Circle
- Area and Perimeter of Quadrilaterals
- Area of Triangles
- Argand Diagram
- Arithmetic Sequences
- Average Rate of Change
- Bijective Functions
- Binomial Expansion
- Binomial Theorem
- Chain Rule
- Circle Theorems
- Circles
- Circles Maths
- Combination of Functions
- Combinatorics
- Common Factors
- Common Multiples
- Completing the Square
- Completing the Squares
- Complex Numbers
- Composite Functions
- Composition of Functions
- Compound Interest
- Compound Units
- Conic Sections
- Construction and Loci
- Converting Metrics
- Convexity and Concavity
- Coordinate Geometry
- Coordinates in Four Quadrants
- Cubic Function Graph
- Cubic Polynomial Graphs
- Data transformations
- De Moivre's Theorem
- Deductive Reasoning
- Definite Integrals
- Deriving Equations
- Determinant of Inverse Matrix
- Determinants
- Differential Equations
- Differentiation
- Differentiation Rules
- Differentiation from First Principles
- Differentiation of Hyperbolic Functions
- Direct and Inverse proportions
- Disjoint and Overlapping Events
- Disproof by Counterexample
- Distance from a Point to a Line
- Divisibility Tests
- Double Angle and Half Angle Formulas
- Drawing Conclusions from Examples
- Ellipse
- Equation of Line in 3D
- Equation of a Perpendicular Bisector
- Equation of a circle
- Equations
- Equations and Identities
- Equations and Inequalities
- Estimation in Real Life
- Euclidean Algorithm
- Evaluating and Graphing Polynomials
- Even Functions
- Exponential Form of Complex Numbers
- Exponential Rules
- Exponentials and Logarithms
- Expression Math
- Expressions and Formulas
- Faces Edges and Vertices
- Factorials
- Factoring Polynomials
- Factoring Quadratic Equations
- Factorising expressions
- Factors
- Finding Maxima and Minima Using Derivatives
- Finding Rational Zeros
- Finding the Area
- Forms of Quadratic Functions
- Fractional Powers
- Fractional Ratio
- Fractions
- Fractions and Decimals
- Fractions and Factors
- Fractions in Expressions and Equations
- Fractions, Decimals and Percentages
- Function Basics
- Functional Analysis
- Functions
- Fundamental Counting Principle
- Fundamental Theorem of Algebra
- Generating Terms of a Sequence
- Geometric Sequence
- Gradient and Intercept
- Graphical Representation
- Graphing Rational Functions
- Graphing Trigonometric Functions
- Graphs
- Graphs and Differentiation
- Graphs of Common Functions
- Graphs of Exponents and Logarithms
- Graphs of Trigonometric Functions
- Greatest Common Divisor
- Growth and Decay
- Growth of Functions
- Highest Common Factor
- Hyperbolas
- Imaginary Unit and Polar Bijection
- Implicit differentiation
- Inductive Reasoning
- Inequalities Maths
- Infinite geometric series
- Injective functions
- Instantaneous Rate of Change
- Integers
- Integrating Polynomials
- Integrating Trig Functions
- Integrating e^x and 1/x
- Integration
- Integration Using Partial Fractions
- Integration by Parts
- Integration by Substitution
- Integration of Hyperbolic Functions
- Interest
- Inverse Hyperbolic Functions
- Inverse Matrices
- Inverse and Joint Variation
- Inverse functions
- Iterative Methods
- Law of Cosines in Algebra
- Law of Sines in Algebra
- Laws of Logs
- Limits of Accuracy
- Linear Expressions
- Linear Systems
- Linear Transformations of Matrices
- Location of Roots
- Logarithm Base
- Logic
- Lower and Upper Bounds
- Lowest Common Denominator
- Lowest Common Multiple
- Math formula
- Matrices
- Matrix Addition and Subtraction
- Matrix Determinant
- Matrix Multiplication
- Metric and Imperial Units
- Misleading Graphs
- Mixed Expressions
- Modulus Functions
- Modulus and Phase
- Multiples of Pi
- Multiplication and Division of Fractions
- Multiplicative Relationship
- Multiplying and Dividing Rational Expressions
- Natural Logarithm
- Natural Numbers
- Notation
- Number
- Number Line
- Number Systems
- Numerical Methods
- Odd functions
- Open Sentences and Identities
- Operation with Complex Numbers
- Operations with Decimals
- Operations with Matrices
- Operations with Polynomials
- Order of Operations
- Parabola
- Parallel Lines
- Parametric Differentiation
- Parametric Equations
- Parametric Integration
- Partial Fractions
- Pascal's Triangle
- Percentage
- Percentage Increase and Decrease
- Percentage as fraction or decimals
- Perimeter of a Triangle
- Permutations and Combinations
- Perpendicular Lines
- Points Lines and Planes
- Polynomial Graphs
- Polynomials
- Powers Roots And Radicals
- Powers and Exponents
- Powers and Roots
- Prime Factorization
- Prime Numbers
- Problem-solving Models and Strategies
- Product Rule
- Proof
- Proof and Mathematical Induction
- Proof by Contradiction
- Proof by Deduction
- Proof by Exhaustion
- Proof by Induction
- Properties of Exponents
- Proportion
- Proving an Identity
- Pythagorean Identities
- Quadratic Equations
- Quadratic Function Graphs
- Quadratic Graphs
- Quadratic functions
- Quadrilaterals
- Quotient Rule
- Radians
- Radical Functions
- Rates of Change
- Ratio
- Ratio Fractions
- Rational Exponents
- Rational Expressions
- Rational Functions
- Rational Numbers and Fractions
- Ratios as Fractions
- Real Numbers
- Reciprocal Graphs
- Recurrence Relation
- Recursion and Special Sequences
- Remainder and Factor Theorems
- Representation of Complex Numbers
- Rewriting Formulas and Equations
- Roots of Complex Numbers
- Roots of Polynomials
- Roots of Unity
- Rounding
- SAS Theorem
- SSS Theorem
- Scalar Triple Product
- Scale Drawings and Maps
- Scale Factors
- Scientific Notation
- Second Order Recurrence Relation
- Sector of a Circle
- Segment of a Circle
- Sequences
- Sequences and Series
- Series Maths
- Sets Math
- Similar Triangles
- Similar and Congruent Shapes
- Simple Interest
- Simplifying Fractions
- Simplifying Radicals
- Simultaneous Equations
- Sine and Cosine Rules
- Small Angle Approximation
- Solving Linear Equations
- Solving Linear Systems
- Solving Quadratic Equations
- Solving Radical Inequalities
- Solving Rational Equations
- Solving Simultaneous Equations Using Matrices
- Solving Systems of Inequalities
- Solving Trigonometric Equations
- Solving and Graphing Quadratic Equations
- Solving and Graphing Quadratic Inequalities
- Special Products
- Standard Form
- Standard Integrals
- Standard Unit
- Straight Line Graphs
- Substraction and addition of fractions
- Sum and Difference of Angles Formulas
- Sum of Natural Numbers
- Surds
- Surjective functions
- Tables and Graphs
- Tangent of a Circle
- The Quadratic Formula and the Discriminant
- Transformations
- Transformations of Graphs
- Translations of Trigonometric Functions
- Triangle Rules
- Triangle trigonometry
- Trigonometric Functions
- Trigonometric Functions of General Angles
- Trigonometric Identities
- Trigonometric Ratios
- Trigonometry
- Turning Points
- Types of Functions
- Types of Numbers
- Types of Triangles
- Unit Circle
- Units
- Variables in Algebra
- Vectors
- Verifying Trigonometric Identities
- Writing Equations
- Writing Linear Equations
- Statistics
- Bias in Experiments
- Binomial Distribution
- Binomial Hypothesis Test
- Bivariate Data
- Box Plots
- Categorical Data
- Categorical Variables
- Central Limit Theorem
- Chi Square Test for Goodness of Fit
- Chi Square Test for Homogeneity
- Chi Square Test for Independence
- Chi-Square Distribution
- Combining Random Variables
- Comparing Data
- Comparing Two Means Hypothesis Testing
- Conditional Probability
- Conducting a Study
- Conducting a Survey
- Conducting an Experiment
- Confidence Interval for Population Mean
- Confidence Interval for Population Proportion
- Confidence Interval for Slope of Regression Line
- Confidence Interval for the Difference of Two Means
- Confidence Intervals
- Correlation Math
- Cumulative Distribution Function
- Cumulative Frequency
- Data Analysis
- Data Interpretation
- Degrees of Freedom
- Discrete Random Variable
- Distributions
- Dot Plot
- Empirical Rule
- Errors in Hypothesis Testing
- Estimator Bias
- Events (Probability)
- Frequency Polygons
- Generalization and Conclusions
- Geometric Distribution
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- Hypothesis Test for Correlation
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- Hypothesis Test of Two Population Proportions
- Hypothesis Testing
- Inference for Distributions of Categorical Data
- Inferences in Statistics
- Large Data Set
- Least Squares Linear Regression
- Linear Interpolation
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- Measures of Central Tendency
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- Point Estimation
- Probability
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- Quantitative Variables
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- Two Categorical Variables
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- Types of Data in Statistics
- Variance for Binomial Distribution
- Venn Diagrams

If you go to buy a car, you know that that car is going to have wheels. Why? Because intuitively you know that since all cars have wheels, the one you wish to buy will too.

How about when you go to a bookstore to buy a physical book, you will always know that that book will have pages. Why? Because intuitively you know that since all physical books have pages, the one you are going to buy will too.

These are examples of how we use deductive reasoning in our lives every day without even realizing it. Not only that, but in a large number of math questions that you have ever answered, you have used deductive reasoning.

In this article, we will go through Deductive reasoning in detail.

**Deductive reasoning** is the drawing of a true conclusion from a set of premises via logically valid steps. A conclusion can be said to be deductively valid if both conclusion and premises are true.

This may seem a tricky concept to grasp at first due to the novel terminology, but it really is quite simple! Any time that you work out an answer with certainty from some initial information, you have used deductive reasoning.

Deductive reasoning really can be understood as drawing facts from other facts, and in essence, is the process of drawing specific conclusions from general premises.

Facts → Facts

General Premises → Specific Conclusions

Let's take a look at some examples of deductive reasoning to make this clearer.

Jenny is told to solve the equation , she uses the following steps,

As Jenny has drawn a true conclusion, , from the initial premise, this is an example of deductive reasoning.

Bobby is asked the question ' *x is** an even number less than 10, not a multiple of 4, and not a multiple of 3. What number is x?' *As it must be an even number less then , Bobby deduces that it must be or As It is not a multiple of or Bobby deduces it cannot be or He decides, therefore, it must be

Bobby has drawn a true conclusion, from the initial premises that is an even number less than that is not a multiple of or Therefore, this is an example of deductive reasoning.

Jessica is told all angles less than are acute angles, and also that angle is She is then asked if angle is an acute angle. Jessica answers that since angle is less than it must be an acute angle.

Jessica has drawn a true conclusion that angle is an acute angle, from the initial premise that all angles less than are acute angles. Therefore, this is an example of deductive reasoning.

Not only are these all examples of deductive reasoning, but did you notice we have **used** deductive reasoning to conclude that they are in fact examples of deductive reasoning. That's enough to make anyone's head hurt!

Some more everyday examples of deductive reasoning might be:

- All tuna have gills, this animal is a tuna - therefore it has gills.
- All brushes have handles, this tool is a brush - therefore it has a handle.
- Thanksgiving is on the 24th of November, today is the 24th of November - therefore today is thanksgiving.

On the other hand, sometimes things that may appear to be sound deductive reasoning, in fact, are not.

Hopefully, you are now familiar with just what deductive reasoning is, but you might be wondering just how you can apply it to different situations.

Well, it would be impossible to cover how to use deductive reasoning in every single possible situation, there are literally infinite! However, it is possible to break it down into a few key tenets that apply to all situations in which deductive reasoning is employed.

In deductive reasoning, it all starts with a **premise** or set of **premises**. These premises are simply statements that are known or assumed to be true, from which we can draw a conclusion through the deductive process. A premise could be as simple as an equation, such as or a general statement, such as *'all cars have wheels*.'

Premises are statements that are known or assumed to be true. They can be thought of as starting points for deductive reasoning.

From this premise or premises, we require to draw a conclusion. To do this, we simply take steps toward an answer. The important thing to remember about deductive reasoning is that **every step must follow logically**.

For instance, all cars have wheels, but that does not mean that logically we can assume anything with wheels is a car. This is a leap in logic and has no place in deductive reasoning.

If we were asked to determine the value of from the premises,

, andthen the logical steps we could take to draw a conclusion about the value of might look like this,

Step 1. Substituting the known values of * *and * *yields * *

Step 2. Simplifying the expression yields * *

Step 3. Subtracting 45 from both sides yields* *

Step 4. Dividing both sides by 4 yields

We can check in this instance that the conclusion we have drawn is in-line with our initial premises by substituting the obtained value of y, as well as the given values of x and z into the equation to see if it holds true.

The equation does hold true! Therefore we know that our conclusion is in-line with our three initial premises.

You can see that each step to reach the conclusion is valid and logical.

For instance, we know in step 3 that if we subtract 45 from both sides, both sides of our equation will remain equal, ensuring that the yielded expression is a true fact. This is a fundamental tenet of deductive reasoning, a step taken to draw a conclusion is valid and logical so long as the statement or expression obtained from it is a true fact.

Let's take a look at some questions that might come up regarding deductive reasoning.

Stan is told that every year for the last five years, the population of grey squirrels in a forest has doubled. At the start of the first year, there were grey squirrels in the forest. He is then asked to estimate how many rabbits there will be years from now.

Stan answers that if the trend of the population doubling every two years continues then the population will be at in years time.

Did Stan use deductive reasoning to reach his answer?

**Solution**

Stan did not use deductive reasoning to reach this answer.

The first hint is the use of the word *estimate* in the question. When using deductive reasoning, we look to reach definite answers from definite premises. From the information given, it was impossible for Stan to work out a definite answer, all he could do was make a good attempt at a guess by assuming that the trend would continue. Remember, we are not allowed to make assumptions in our steps when using deductive reasoning.

Prove with deductive reasoning that the product of an odd and even number is always even.

**Solution**

We know that even numbers are integers that are divisible by , in other words is a factor. Therefore we can say that even numbers are of the form where is any integer.

Similarly, we can say that any odd number is some even number plus so we can say that odd numbers are of the form , where is any integer.

The product of any odd and even number therefore can be expressed as

Then we can expand through to get,

And factor out the 2 to get,

Now, how does this prove that the product of an odd and even number is always even? Well, let's take a closer look at the elements inside the brackets.

We already said that and were just integers. So, the product of and , that is is also just an integer. What happens if we add two integers, , together? We get an integer! Therefore our final answer is of the even number form we introduced at the beginning, .

We have used deductive reasoning in this proof, as in each step we have used sound logic and made no assumptions or leaps in logic.

Find, using deductive reasoning, the value of A, where

repeated to infinity.

**Solution**

One way to solve this, is to first take away from one.

Then, by expanding the brackets on the right-hand side we get,

Hmmm, does that right-hand side seem familiar? It's just of course! Therefore

Which we can simplify to

Hmmm, that's odd! It's not an answer that you would expect. In fact, this particular series is known as *Grandi's Series*, and there is some debate amongst mathematicians over whether the answer is 1, 0, or 1/2. This proof however is a good example of how deductive reasoning can be used in math to seemingly prove strange and unintuitive concepts, sometimes it's just about thinking outside of the box!

There are three primary types of deductive reasoning, each with its own fancy-sounding name, but really they are quite simple!

If and then This is the essence of any **syllogism**. A syllogism connects two separate statements and connects them together.

For instance, if Jamie and Sally are the same age, and Sally and Fiona are the same age, then Jamie and Fiona are the same age.

An important example of where this is used is in thermodynamics. The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.

A implies B, since A is true then B is also true. This is a slightly complicated way of terming the simple concept of **modus ponens.*** *

An example of a *modus ponens* could be, all shows on a tv channel are less than forty minutes long, you are watching a show on that tv channel, therefore the show you are watching is less than forty minutes long.

A *m**odus ponens* affirms a conditional statement. Take the previous example. The conditional statement implied in the example is '*if the show is on this tv channel, then it is less than forty minutes long.'*

*Modus tollens *are similar, but opposite to *modus ponens*. Where *modus ponens* affirm a certain statement, *modus ponens* refute it.

For instance, in Summer the sun sets no earlier than 10 o'clock, today the sun is setting at 8 o'clock, therefore it is not Summer.

Notice how *modus tollens* are used to make deductions that disprove or discount something. In the example above, we have used deductive reasoning in the form of a *modus tollens *not to deduce what season it is, but rather what season it is not.

Which type of deductive reasoning has been used in the following examples?

**(a)** and , therefore .

**(b) **All even numbers are divisible by two, is divisible by two - therefore is an even number.

**(c) **All planes have wings, the vehicle I am on does not have wings - therefore I am not on a plane.

**(d) **All prime numbers are odd, 72 is not an odd number, 72 cannot be a prime number.

**(e) **Room A and Room B are at the same temperatures, and Room C is the same temperature as Room B - therefore Room C is also the same temperature as Room A

**(f) **All fish can breathe underwater, a seal cannot breathe underwater, therefore it is not a fish.

**Solution**

**(a) **Syllogism - as this deductive reasoning is of the form and , therefore

**(b)** Modus Ponens - as this deductive reasoning is affirming something about

**(c)** Modus Tollens - as this deductive reasoning is refuting something about

**(d)** Modus Tollens - once again this deductive reasoning is refuting something about

**(e)** Syllogism - this deductive reasoning is also of the form and therefore

**(f) **Modus Ponens - this deductive reasoning is affirming something about

- Deductive reasoning is a type of reasoning that draws true conclusions from equally true premises.
- In deductive reasoning, logical steps are taken from premise to conclusion, with no assumptions or leaps in logic made.
- If a conclusion has been reached using flawed logic or assumption then invalid deductive reasoning has been used, and the conclusion drawn cannot be considered true with certainty.
- There are three types of deductive reasoning: syllogism, modus ponens, and modus tollens.

Deductive reasoning is a type of reasoning that draws true conclusions from equally true premises.

Deductive and inductive reasoning are both used to draw conclusions from a set of premises.

More about Deductive Reasoning

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