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Q16P

Expert-verifiedFound in: Page 14

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

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

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.

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.

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.

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.

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