Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20208 Jan 2020Morning ShiftMathematicsMathematical ReasoningActual

Which one of the following is a tautology?

Options

  1. Ap ∧ p → q → q
  2. Bq → p ∧ p → q
  3. Cp ∧ p ∨ q
  4. Dp ∨ p ∧ q

Correct answer

A. p ∧ p → q → q

Step-by-step solution

p q p → q p ∧ p ∧ → q p ∧ p → q → q q → p ∧ p → q p ∧ q p ∨ p ∧ q p ∨ q p ∧ p ∨ q T T T T T T T T T T T F F F T T F T T T F T T F T F F F T F F F T F T T F F F F

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