Question

Which of the following illustrates the truth value of the given conditional statement? If a week has seven days, then a year has twenty months.

1. T F -> F
2.T T -> T
3.F T -> T
4.F F -> F

Answer 1

Answer: The correct option is (1) T F ⇒ F.

Step-by-step explanation: We are given to select the correct illustration of the truth value of the following conditional statement :

"If a week has seven days, then a year has twenty months."

Let us consider that

p : A week has seven days. It is true.

q : A year has twenty months. It is false.

The truth table for the conditional statement p ⇒ q i as follows :

p q p ⇒ q

T T T

T F F

F T T

F F T

Since p is true and q is false, so the required illustration is

T F ⇒ F.

Option (1) is CORRECT.

Answer 2

1. T F ⇒ F

Explanation:

The conditional statement is,

"If a week has seven days, then a year has twenty months."

Let, p-If a week has seven days and q-A year has twenty months

We have that 'p' is true and 'q' is false. Then, 'pq' is represented by 'T F'.

Since, the conclusion is,

'If a week has seven days, then a year has twenty months', which is not true.

Thus, p ⇒ q is false i.e. It is represented by F.

Hence, the truth value of the given statement is 'T F ⇒ F'.