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Mathematics

Assertion (A): If x is an irrational number, 1x\dfrac{1}{x} is not irrational.

Reason (R): Reciprocal of every irrational number is irrational.

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

Rational Irrational Nos

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Answer

A is false, R is true.

Explanation

Given,

x is an irrational number.

Let x = 2\sqrt2

And, 1x=12=1×22×2=22\dfrac{1}{x} = \dfrac{1}{\sqrt2} = \dfrac{1 \times \sqrt2}{\sqrt2 \times \sqrt2} = \dfrac{\sqrt2}{2}

22\dfrac{\sqrt2}{2} is also irrational number.

∴ Reciprocal of every irrational number is irrational.

∴ Assertion(A) is false.

Given,

Reciprocal of every irrational number is irrational.

∴ Reason(R) is true.

Hence, Assertion (A) is false and Reason (R) is true.

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