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JEE Main2008MathematicsMathematical ReasoningActual

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) .

Options

  1. AStatement -1 is false, Statement -2 is true
  2. BStatement -1 is true, Statement -2 is true, Statement -2 is a correct explanation for Statement -1
  3. CStatement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1 .
  4. DStatement -1 is true, Statement -2 is false.

Correct answer

D. Statement -1 is true, Statement -2 is false.

Step-by-step solution

Given statement r= p q Statement -1: r₁=(p q) ( p q) Statement -2: r₂= (p q)=(p q) ( q p) From the truth table of r, r₁ and r₂ , r=r₁ . Hence Statement -1 is true and Statement -2 is false.

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