Question

# Let p be the statement x is an irrational number, q be the statement y is a transcendental number, and r be the statementx 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 $$\sim (p\leftrightarrow \sim q)$$

A
Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
B
Statement-1 is true, Statement-2 is false.
C
Statement-1 is false, Statement-2 is true.
D
Both statement 1 and 2 are false.

Solution

## The correct option is D Both statement 1 and 2 are false.p : x is an irrational numberq : y is a transcendental numberr : x is a rational number iff y is a transcendental number $$\Rightarrow r : \sim p\leftrightarrow q$$ $$s_{1}$$ : q or p  $$s_{2}$$ : $$\sim (p\leftrightarrow \sim q)$$ Clearly $$s_{1}$$ and r are not equivalent $$\Rightarrow$$ Statement-1 is false.Also  $$s_{2}$$ and r are not equivalent  $$\Rightarrow$$ Statement-2 is also false. Hence none of the statement is correct.  Maths

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