Mathematical Logic And Boolean Algebra Question 39
Question: Which of the following statement is a contradiction?
Options:
A) $ (\tilde{\ }p\vee \tilde{\ }q)\vee (p\vee \tilde{\ }q) $
B) $ (p\to q)\vee (p\wedge \tilde{\ }q) $
C) $ (\tilde{\ }p\wedge q)\wedge (\tilde{\ }q) $
D) $ (\tilde{\ }p\wedge q)\vee (\tilde{\ }q) $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] We consider following truth table. $ p $ $ q $ $ \tilde{\ }p $ $ \tilde{\ }q $ $ p\wedge q $ $ p\vee q $ $ (\tilde{\ }(p\vee q) $ $ (p\wedge q)\wedge $ $ (\tilde{\ }(p\vee q) $ T T F F T T F F T F F T F T F F F T T F F T F F F F T T F F T F Clearly last column of the above truth table contains only F. Hence $ (p\wedge q)\wedge (\tilde{\ }(p\vee q) $ is a contradiction
BETA
