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

The negation of ∽ s ∨ ∽ r ∧ s is equivalent to

Options

  1. As   ∧   r
  2. Bs ∧ ~ r
  3. Cs ∧ r ∧ ~ s
  4. Ds ∨ r ∨ ~ s

Correct answer

A. s   ∧   r

Step-by-step solution

Given ∽ ∽ s ∨ ∽ r ∧ s = s ∧ ∽ ∽ r ∧ s ∵ ~ p ∧ q = ∽ p ∨ ∽ q and ∽ p ∨ q = ∽ p ∧ ∽ q = s ∧ r ∨ ∽ s = s ∧ r ∨ s ∧ ∽ s = s ∧ r ∨ F = s ∧ 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