Question

The contrapositive of the statement "If the number is not divisible by 3, then it is not divisible by 15" is

• A. If the number is not divisible by 3,then it is not divisible by 15
• B. If the number is not divisible by 15,then it is not divisible by 3
• C. If the number is not divisible by 15,then it is divisible by 3
• D. If the number is divisible by 15,then it is divisible by 3
• E. If the number is divisible by 15,then it is not divisible by 3

Answer 1

The Correct Option is D

Original statement: "If the number is not divisible by 3, then it is not divisible by 15"

In logical form:
Let \( P \): "divisible by 3", \( Q \): "divisible by 15"
Statement: \( \neg P \rightarrow \neg Q \)

Contrapositive rule:
The contrapositive of \( A \rightarrow B \) is \( \neg B \rightarrow \neg A \)
Thus, contrapositive of \( \neg P \rightarrow \neg Q \) is \( Q \rightarrow P \)

Translated back:
"If the number is divisible by 15 (\( Q \)), then it is divisible by 3 (\( P \))"

Correct option: (D)

Answer 2

Let \( P \) be the statement "the number is not divisible by 3" and \( Q \) be the statement "the number is not divisible by 15".

The original statement is "If \( P \), then \( Q \)". The contrapositive of this statement is "If not \( Q \), then not \( P \)".

In words:

• Original statement: If a number is not divisible by 3, then it is not divisible by 15.
• Contrapositive: If a number is divisible by 15, then it is divisible by 3.

Therefore, the correct answer is (D).