Mathematical Logic And Boolean Algebra Question 60

Question: If $ p\Rightarrow (q\vee r) $ is false, then the truth values of $ p,q,r $ are respectively

Options:

A) $ T,F,F $

B) $ F,F,F $

C) $ F,T,T $

D) $ T,T,F $

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $ p\Rightarrow q $ is false only when p is true and q is false.
$ \therefore p\Rightarrow q $ is false when p is true and $ q\vee r $ is false, and $ q\vee r $ is false when both q and r are false.