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Closure Property of Rational Numbers

Study the fol...

Question

Study the following statements.
Statement - 1 : Rational numbers are always closed under division.
Statement - 2 : Division by zero is not defined.
Which of the following options hold?

Both statement - 1 and statement - 2 are true.

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Statement - 1 is true but statement -2 is false.

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Statement - 1 is false but statement -2 is true.

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Both statement - 1 and statement - 2 are false.

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Solution

The correct option is B Statement - 1 is false but statement -2 is true.
Statement $1 :$ Rational number can even be simply integers which can be further represented as $\frac{p}{q}$ form. So, statement $1$ is false.
Statement $2 :$ Any number divided by $0$ is not defined. So, statement $2$ is true.

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