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JEE Main 20199 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
9 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2019 · 9 April · Evening Shift · Mathematics · Mathematical Reasoning

If p ⇒ (q ∨ r) is False , then the truth values of p, q, r are...

If p⇒p ⇒\left(q ∨ r\right)isisFalse,thenthetruthvaluesof, then the truth values ofp, q, rarerespectively,(whereare respectively, (whereTisisTrue and FF is FalseFalse)

Options

  1. AT,F,FT, F, F
  2. BF,T,TF, T, T
  3. CF,F,FF, F, F
  4. DT,T,FT, T, F

Correct answer

A. T,F,FT, F, F

Step-by-step solution

We know that the conditional statement a⇒ba ⇒ b is FalseFalse only when aa is FalseFalse and bb is True.True .

Hence, p⇒(q∨r):Falsep ⇒ ( q ∨ r ) : False when p:True;q∨r:Falsep: True; q ∨ r: False

Again, we know that a∨ba ∨ b is FalseFalse when both a and ba \text{ and } b are false.

Hence, p:True;q:False;r:False.p: True; q: False; r: False .

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