Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202127 Aug 2021Morning ShiftMathematicsMathematical ReasoningActual

The statement ( p ∧ ( p → q ) ∧ ( q → r ) ) → r is

Options

  1. Aa tautology
  2. Bequivalent to q → ~ r
  3. Ca fallacy
  4. Dequivalent to p → ~ r

Correct answer

A. a tautology

Step-by-step solution

Let f = ( p ∧ ( p → q ) ∧ ( q → r ) ) Make truth table, r p q p → q q → r f f → r T T T T T T T F T T T F F T T T F F T F T F T F F T F T T F T T T F T F F T T F F T T F F F T F T F F F F T F T So, the answer is tautology.

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