Q82.Let p be the statement " x is an irrational number", q be the statement " y is a transcendental number", and r be the statement " x is a rational number iff y is a transcendental number". Statement −1 : r is equivalent to either q or p Statement −2 : r is equivalent to ∼(p ↔∼q). (1) Statement −1 is false, Statement −2 is true (2) Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1 (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1.

Q83.The statement p →(q →p) is equivalent to (1) p →(p →q) (2) p →(p ∨q) (3) p →(p ∧q) (4) p →(p ↔q)

Q70.Statement-1: ∼(p ↔∼q) is equivalent to p ↔q . Statement-2 : ∼(p ↔∼q) is a tautology. (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true

Q73.Let S be a non-empty subset of R. Consider the following statement: P : There is a rational number x ∈S such that x > 0. Which of the following statements is the negation of the statement P ? JEE Main 2010 JEE Main Previous Year Paper (1) There is no rational number x ∈S such that (2) Every rational number x ∈S satisfies x ≤0 x ≤0 (3) x ∈S and x ≤0 ⇒x is not rational (4) There is a rational number x ∈S such that x ≤0