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JEE Main 201325 AprilOnline
Exam
JEE Main
Year
2013
Date
25 April
Mode
Online
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2013 · 25 April · Online · Mathematics · Mathematical Reasoning

Let p and q be any two logical statements and r: p arrow( p q) . If...

Let pp and qq be any two logical statements and r:p→(∼p∨q)\mathrm{r}: \mathrm{p} \rightarrow(\sim p \vee q). If rr has a truth value FF, then the truth values of pp and qq are respectively:

Options

  1. AF,F\mathrm{F}, \mathrm{F}
  2. BT,T\mathrm{T}, \mathrm{T}
  3. CT, F
  4. DF, T

Correct answer

C. T, F

Step-by-step solution

p→(∼p∨q)p \rightarrow(\sim p \vee q) has truth value F\mathrm{F}. It means p→(∼p∨q)p \rightarrow(\sim p \vee q) is false. It means pp is true and ∼p∨q\sim p \vee q is false. ⇒p\Rightarrow p is true and both ∼p\sim p and qq are false. ⇒p\Rightarrow p is true and qq is false.
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