Under which operator is the set of rational numbers not closed-AdditionSubtractionMultiplicationDivision

The correct option is D DivisionSet of rational numbers is not closed under nbsp;division. Suppose that 'a' is a rational number. Then, 0/a is a rational nu ...

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Standard VIII

Mathematics

Closure Property of Rational Numbers

Under which o...

Question

Under which operator is the set of rational numbers not closed?

Addition

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Subtraction

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Multiplication

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Division

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Solution

The correct option is D Division
Set of rational numbers is not closed under division.

Suppose that 'a' is a rational number.
Then, $\frac{0}{a}$ is a rational number but $\frac{a}{0}$ is not.
So, rational numbers are not closed under division.

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Similar questions

Question 4
Which of the following is not true?
(a) rational numbers are closed under addition.
(b) rational numbers are closed under subtraction.
(c) rational numbers are closed under multiplication.
(d) rational numbers are closed under division.

Q. On Q, the set of all rational numbers a binary operation * is defined by

a * b = \frac{a + b}{2}

.
Show that * is not associative on Q.

Q. Under which operator is the set of rational numbers not closed?

Rational numbers are not closed under which operation?

Q. Under which of the following operations, are the rational numbers not closed?

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Under which operator is the set of rational numbers not closed?

The correct option is D DivisionSet of rational numbers is not closed under division. Suppose that 'a' is a rational number. Then, 0a is a rational number but a0 is not. So, rational numbers are not closed under division.

The correct option is D Division
Set of rational numbers is not closed under division.

Suppose that 'a' is a rational number.
Then, $\frac{0}{a}$ is a rational number but $\frac{a}{0}$ is not.
So, rational numbers are not closed under division.