JEE Main 2015MathematicsMathematical ReasoningEasyMCQ

JEE Main 2015 — Mathematical Reasoning Question with Solution

JEE Main 2015 (11 Apr Online)

Question

Consider the following statements:

P: Suman is brilliant

Q: Suman is rich

R: Suman is honest

The negation of the statement, "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as

Choose an option

Show full solutionCorrect option: C
Correct answer
C~Q↔P∧~R

Step-by-step explanation

P : Suman is brilliant 

~ P : Suman is not brilliant

Q = Suman is rich 

~ Q : Suman is not rich 

R : Suman is honest 

~ R : Suman is not honest 

Also, ~p⇔q≡~p⇔q≡p⇔~q

Hence  ~(P∧∼R)⟷Q is ∼Q⟷P∧∼R

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About this question

This is a previous-year question from JEE Main 2015, covering the Mathematical Reasoning chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.