Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2015MathematicsMathematical ReasoningActual

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

Options

  1. A~ Q ↔ ~ P ∨ R
  2. B~ Q ↔ P ∨ ~ R
  3. C~ Q ↔ P ∧ ~ R
  4. D~ Q ↔ ~ P ∧ R

Correct answer

C. ~ Q ↔ P ∧ ~ R

Step-by-step solution

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   i s   ∼ Q ⟷ P ∧ ∼ R

Practice Mathematical Reasoning on Quantrex Academy →

More from Mathematical Reasoning

Negation of p ∧ q ∧ ~ p ∧ q is 2023The statement ( p ∧ ( ~ q ) ) ∨ ( ( ~ p ) ∧ q ) ∨ ( ( ~ p ) ∧ ( ~ q ) ) is equivalent to _ _ _ _ _ 2023The negation of the statement ( ( A ∧ ( B ∨ C ) ) ⇒ ( A ∨ B ) ) ⇒ A is 2023Among the two statements S 1 : p ⇒ q ∧ p ∧ ~ q is a contradiction and S 2 : p ∧ q ∨ ~ p ∧ q ∨ p ∧ ~ q ∨ ~ p ∧ ~ q is a t 2023The converse of ~ p ∧ q ⇒ r is 2023The number of ordered triplets of the truth values of p , q and r such that the truth value of the statement p ∨ q ∧ p ∨ r ⇒ q ∨ r is True, is equal t 2023The statement ~ p ∨ ~ p ∧ q is equivalent to 2023The negation of the statement p ∨ q ∧ q ∨ ~ r is 2023 Full Mathematical Reasoning list All JEE Main PYQs