Mathematical Logic And Boolean Algebra Question 49
Question: Which of the following is always true?
Options:
A) $ (\tilde{\ }p\vee \tilde{\ }q)\equiv (p\wedge q) $
B) $ (p\to q)\equiv (\tilde{\ }q\to \tilde{\ }p) $
C) $ \tilde{\ }(p\to \tilde{\ }q)\equiv (p\wedge \tilde{\ }q) $
D) $ \tilde{\ }(prightarrow q)\equiv (p\to q)\to (q\to p) $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Since $ \tilde{\ }(p\vee q)\equiv (\tilde{\ }p\wedge \tilde{\ }q) $ and $ \tilde{\ }(p\wedge q)\equiv (\tilde{\ }p\vee q) $ So option [b] and [d] are not true. $ (p\to q)\equiv p\wedge \tilde{\ }q), $ So option [c] is not true. Now $ p\to q\tilde{\ }p\vee q $ $ \tilde{\ }q\to \tilde{\ }p\equiv [\tilde{\ }(\tilde{\ }q)\vee \tilde{\ }p]\equiv q\vee \tilde{\ }p\equiv \tilde{\ }p\vee q $ $ p\to q\equiv \tilde{\ }q\to \tilde{\ }p $
BETA
