Mathematical Logic And Boolean Algebra Question 2
Question: Which of the following is false?
Options:
A) $ p\vee \tilde{\ }p $ is a tautology
B) $ \tilde{\ }(\tilde{\ }p)rightarrow p $ is a tautology
C) $ p\wedge \tilde{\ }p $ is a contradiction
D) $ ((p\wedge q)\to q)\to p $ is a tautology
Show Answer
Answer:
Correct Answer: D
Solution:
[d] The truth value of $ \tilde{\ }(\tilde{\ }p)rightarrow p $ as follow $ p $ $ \tilde{\ }p $ $ \tilde{\ }(\tilde{\ }p) $ $ \tilde{\ }(\tilde{\ }p)\to p $ $ p\to $ $ \tilde{\ }(\tilde{\ }p) $ $ \tilde{\ }(\tilde{\ }p) $ $ rightarrow p $ T F T T T T F T F T T T Since last column of above truth table contains only T Hence $ \tilde{\ }(\tilde{\ }p)\to p $ is a tautology.
BETA
