Question

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$\mathbf{2}\mathbf{>}\mathbf{1}$

Short answer

a) True

b) False

c) True

d) False

Step-by-step solution

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.

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.

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.

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.