Question

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

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

Short answer

1. False
2. True
3. True
4. True

Step-by-step solution

Definition of the 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,

$1+1=3$is false hence, truth value is true.

Truth value for b)

We write given expressions as,

$1+1=3$is false hence, truth value is true.

Truth value for c)

We write given expressions as,

$1+1=2$is true and dogs can fly is false

If true then false is false.

Hence, truth value is false.

Truth value for d)

We write given expressions as,

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

If true then true is true.

Hence, truth value is true.