Short Answer

There are infinitely many stations on a train route. Sup-
pose that the train stops at the first station and suppose that if the train stops at a station, then it stops at the next station. Show that the train stops at all stations.

Examples of Hypothesis In the conditional, "If all four sides of a quadrilateral measure the same, then the quadrilateral is a square" the hypothesis is "all four sides of a quadrilateral measure the same".

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 2

Let p(k) be the hypothesis that the train stops at station k.

Base case: P(1) is true because we are told that the train stops at the first station.

Induction step: Assume that the train stops at station k - 1 that is P ( k - 1 ) , is true.

Now, we are told to assume that, if the train stops at a station, then it stops at the next station. Since we assumed that it stopped at station k - 1 (by induction hypothesis), it means that it will stop at station k. Thus P (K) , is true.

Then, by induction, P(k) is true for all k and, therefore, the train stops at all stations.

Find Study Materials for

Create Study Materials

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

There are infinitely many stations on a train route. Sup-
pose that the train stops at the first station and suppose that if the train stops at a station, then it stops at the next station. Show that the train stops at all stations.

Step by Step Solution

Step 2

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

There are infinitely many stations on a train route. Sup-pose that the train stops at the first station and suppose that if the train stops at a station, then it stops at the next station. Show that the train stops at all stations.

Step by Step Solution

Step 2

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

There are infinitely many stations on a train route. Sup-
pose that the train stops at the first station and suppose that if the train stops at a station, then it stops at the next station. Show that the train stops at all stations.