Ask Questions, Get Answers

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

Choose the correct answer. The statement $p \rightarrow (q \rightarrow p)$ is equivalent to which of the following?

$\begin{array}{1 1} (A) p \rightarrow (p \rightarrow q) \\(B) p \rightarrow (p \vee q) \\ (C) p \rightarrow (p \wedge q) \\ (D) p \leftrightarrow (p \rightarrow q)\end{array}$

Can you answer this question?

1 Answer

0 votes
$p \rightarrow (q \rightarrow p) \equiv \sim p \vee (q \rightarrow p)$ $\equiv \sim p \vee (\sim q \vee p)$
$\qquad \equiv \sim q \vee (p \vee \sim p ) \equiv \sim q \vee T = T$
$\Rightarrow p \rightarrow (q \rightarrow p) $ is a tautology.
Also, $p \rightarrow (p\vee q) \equiv \sim p \vee (p \vee q ) \equiv (~p \vee p) \vee q \equiv T \vee q \equiv T$
$\Rightarrow p \rightarrow (p \vee q ) $ is also a tautology.
$\Rightarrow p \rightarrow (q \rightarrow p) \equiv p \rightarrow (p \vee q ) $
answered Mar 20, 2014 by balaji.thirumalai

Related questions

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