Question

Negation of the statement "If an integer is greater than 4 and less than 5, then it is a multiple of 3", is

• A. An integer is not greater than 4 but less than 5 and it is a multiple of 3.
• B. If an integer is not greater than 4 and less than 5 then it is not a multiple of 3.
• C. An integer is greater than 4 and less than 5 but it is not a multiple of 3.
• D. An integer is not greater than 4 and not less than 5 but it is not a multiple of 3.

Hint:

The negation of "if P then Q" is "P and not Q".

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
A conditional \(P \to Q\) is false only when P is true and Q is false. So \(\sim(P \to Q) \equiv P \wedge \sim Q\).

Step 2: Identify P and Q
P: "an integer is greater than 4 and less than 5". Q: "it is a multiple of 3".

Step 3: Form the negation
The negation keeps P as it is and negates Q: "An integer is greater than 4 and less than 5 but it is not a multiple of 3."
Options (A) and (D) change P, option (B) is another conditional and not a negation of the original.

Final Answer:
The negation is option (C). \[ \boxed{P \wedge \sim Q} \]