Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

The proposition $(P \vee Q) \vee (\sim P \wedge \sim Q)$ is a:

(A) contradiction (B) tautology (C) neither a contradiction nor a tautology (D) both a contradiction nor a tautology
Can you answer this question?

1 Answer

0 votes
Let us construct the truth table for this proposition:
$ \begin{matrix} P & Q & P\vee Q & \sim P & \sim Q & \sim P \wedge \sim Q & (P \vee Q) \vee (\sim P\; \wedge \sim Q)\\ T & T &T & F & F & F &T \\ F& T & T &T & F &F & T\\ T&F & T & F & T&F &T \\ F& F & F & T& T &T &T \end{matrix}$
Since the proposition is True for every assignment of truth values to its components, it is a tautology.
answered Mar 20, 2014 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App