Mathematical Logic And Boolean Algebra Question 132

Question: The negation of the statement “If I become a teacher, then I will open a school”, is:

Options:

A) I will become a teacher and I will not open a school.

B) Either I will not become a teacher or I will not open a school.

C) Nither I will not become a teacher or I will not open a school

D) I will not become a teacher or I will open a school.

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Let p : I become a teacher q: I will open a school Negation of $ p\to q $ is $ \sim (p\to q)=p\wedge \sim q $ i.e., I will become a teacher and I will not open a school.