Question

Which of the following illustrates the truth value of the given conditional statement?

p: 10 > 7
q: 10 > 5
q → p
Option 1: T → T
Option 2: T → F
Option 3: F → T
Option 4: F → F

Answer 1

The truth value of the conditional statement 'If 10 > 5, then 10 > 7' is true. Statement p (10 > 7) and statement q (10 > 5) are both true, so the correct illustration is Option 1: T → T.

Step-by-step explanation:

The statement 'q → p' translates to 'If 10 > 5, then 10 > 7.'

To determine its truth value, we evaluate both parts of the conditional:

• Statement p ('10 > 7') is true.
• Statement q ('10 > 5') is also true.

In a conditional statement, if the hypothesis (in this case q) is true and the conclusion (in this case p) is also true, the conditional statement is true.

Therefore, the truth value of the statement 'q → p' is true.

The correct illustration of the truth value for the conditional statement 'q → p' is Option 1: T → T, meaning that both the hypothesis and the conclusion are true.