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JEE Main 201412 AprilOnline
Exam
JEE Main
Year
2014
Date
12 April
Mode
Online
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2014 · 12 April · Online · Mathematics · Mathematical Reasoning

Let p, q, r denote arbitrary statements. Then the logically...

Let p,q,r\mathrm{p}, \mathrm{q}, \mathrm{r} denote arbitrary statements. Then the logically equivalent of the statement p⇒(q∨r)\mathrm{p} \Rightarrow(\mathrm{q} \vee \mathrm{r}) is:

Options

  1. A(p∨q)⇒r(\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}
  2. B(p⇒q)∨(p⇒r)(\mathrm{p} \Rightarrow \mathrm{q}) \vee(\mathrm{p} \Rightarrow \mathrm{r})
  3. C(p⇒∼q)∧(p⇒r)(\mathrm{p} \Rightarrow \sim \mathrm{q}) \wedge(\mathrm{p} \Rightarrow \mathrm{r})
  4. D(p⇒q)∧(p⇒∼r)(\mathrm{p} \Rightarrow \mathrm{q}) \wedge(\mathrm{p} \Rightarrow \sim \mathrm{r})

Correct answer

B. (p⇒q)∨(p⇒r)(\mathrm{p} \Rightarrow \mathrm{q}) \vee(\mathrm{p} \Rightarrow \mathrm{r})

Step-by-step solution

Given statement is p⇒(q∨r)p \Rightarrow(q \vee r) which is equivalent to (p \Rightarrow q) \vee(p \Rightarrow r)
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