Mathematical Logic And Boolean Algebra Question 156

Question: Negation of the conditional : ?If it rains, I shall go to school? is

Options:

A) It rains and I shall go to school

B) It rains and I shall not go to school

C) It does not rains and I shall go to school

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

p : It rains, q : I shall go to school Thus, we have $ p\Rightarrow q $ Its negation is $ \tilde{\ }(p\Rightarrow q) $ i.e. $ p\ \wedge \tilde{\ }q $ i.e. It rains and I shall not go to school.