• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q16P

Expert-verified Found in: Page 14 ### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095 # Determine whether these biconditionals are true or false. a) ${\mathbf{2}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{2}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{4}}$ if and only if ${\mathbf{1}}{\mathbf{+}}{\mathbf{1}}{\mathbf{=}}{\mathbf{2}}$ b) ${\mathbf{1}}{\mathbf{+}}{\mathbf{1}}{\mathbf{=}}{\mathbf{2}}$ if and only if ${\mathbf{2}}{\mathbf{+}}{\mathbf{3}}{\mathbf{=}}{\mathbf{4}}$ c) ${\mathbf{1}}{\mathbf{+}}{\mathbf{1}}{\mathbf{=}}{\mathbf{3}}$ if and only if monkeys can fly. d) ${\mathbf{0}}{\mathbf{>}}{\mathbf{1}}$if and only if ${\mathbf{2}}{\mathbf{>}}{\mathbf{1}}$

a) True

b) False

c) True

d) False

See the step by step solution

## Step1: Definition of the biconditional

A bi-conditional statement is a combination of two conditional statements and its converse is written in if and only if form.

## Step 2: Truth value for a)

We write given expressions as,

$2+2=4$is true and $1+1=2$ is also true.

True if and only if true is True.

Hence, truth value is True.

## Step 3:Truth value for b)

We write given expressions as,

$1+1=2$ is true and $2+3=4$ is false.

True if and only if false is false.

Hence, truth value is False.

## Step 4: Truth value for c)

We write given expressions as,

$1+1=3$ is false and monkeys can fly is also false.

False if and only if false is true.

Hence, truth value is True.

## Step 5: Truth value for d)

We write given expressions as,

$0>1$ is false and $2>1$ is true

False if and only if true is false.

Hence, truth value is false. ### Want to see more solutions like these? 