Question

Determine whether each of these conditional statements is true or false.

a) If$\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{2}$, then$\mathbf{2}\mathbf{+}\mathbf{2}\mathbf{=}\mathbf{5}$.
b) If$\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{3}$, then$\mathbf{2}\mathbf{+}\mathbf{2}\mathbf{=}\mathbf{4}$.
c) If$\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{3}$, then$\mathbf{2}\mathbf{+}\mathbf{2}\mathbf{=}\mathbf{5}$.
d) If monkeys can fly, then$\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{3}$.

Short answer

a) False

b) True

c) True

d) True

Step-by-step solution

Definition of conditional statement

A conditional statement is a statement which is written in the form,

“If P then Q,” where P and Q are sentences.

Truth value for a)

We write given expressions as,

$1+1=2$is true and$2+2=5$is false.

If true then false is false.

Hence, truth value is false.

Step 3:Truth value for b)

We write given expressions as,

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

If false then true is true.

Hence, truth value is true.

Truth value for c)

We write given expressions as,

$1+1=3$is false and is$2+2=5$also false

If false then false is true.

Hence, truth value is True.

Truth value for d)

We write given expressions as,

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

If false then false is true

Hence, truth value is true.