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: Rule
Not(if P then Q) means P holds and Q fails.

Step 2: Apply
P stays: integer greater than 4 and less than 5. Q becomes: not a multiple of 3.

Step 3: Select
That is exactly option (C).

Final Answer:
Option (C). \[ \boxed{P \wedge \sim Q} \]