Verified Solution • 2025–26 Session moderate

QJEEM11Ma6856: JEE Main 2011 Mathematics - Class 11 JEEM11Ma6856 Solution: Consider the following statements P : Suman is brilliant Q :…

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 expressed as :

Multiple Choice Options

  • A ∼[Q↔(P∧∼R)]
  • B ∼Q↔P∧R
  • C ∼(P∧∼R)↔Q
  • D ∼P∧(Q↔∼R)

Step-by-Step Verified Solution

"Suman is brilliant and dishonest" an be expressed as : P∧∼R

So “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as :

(P∧∼R)↔Q

Now negation of this = ∼[(P∧∼R)↔Q]

You should know, p↔q≡q↔p

So, ∼[(P∧∼R)↔Q]≡∼[Q↔(P∧∼R)]

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