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JEE Main 201411 AprilOnline
Exam
JEE Main
Year
2014
Date
11 April
Mode
Online
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2014 · 11 April · Online · Mathematics · Mathematical Reasoning

The proposition (p q) (p q) is logically equivalent to:

The proposition ∼(p∨∼q)∨∼(p∨q)\sim(p \vee \sim q) \vee \sim(p \vee q) is logically equivalent to:

Options

  1. Ap\mathrm{p}
  2. Bq\mathrm{q}
  3. C∼p\sim \mathrm{p}
  4. D∼q\sim \mathrm{q}

Correct answer

C. ∼p\sim \mathrm{p}

Step-by-step solution

Given ∼(p∨∼q)∨∼(p∨q)\sim(p \vee \sim q) \vee \sim(p \vee q)≡(∼p∨q)∨(∼p∨∼q)≡∼p∨(q∨∼q)≡∼p\begin{aligned} &\equiv(\sim p \vee q) \vee(\sim p \vee \sim q) \\ &\equiv \sim p \vee(q \vee \sim q) \\ &\equiv \sim p \end{aligned}$$
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