If $D$ be subset of the set of all rational numbers which can be expressed as terminating decimals, then $D$ is closed under the binary operations of:

addition, subtraction and division

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addition, multiplication and division

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addition, subtraction and multiplication

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subtraction, multiplication and division

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Solution

The correct option is C addition, subtraction and multiplication
Division of rational number that can be expressed as terminating decimal may not be rational. $∴$ $D$ is closed under addition, subtraction, and multiplication.

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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.

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Q. Question 104
Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.

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If D be subset of the set of all rational numbers which can be expressed as terminating decimals, then D is closed under the binary operations of:

The correct option is C addition, subtraction and multiplicationDivision of rational number that can be expressed as terminating decimal may not be rational. ∴ D is closed under addition, subtraction, and multiplication.

If $D$ be subset of the set of all rational numbers which can be expressed as terminating decimals, then $D$ is closed under the binary operations of:

The correct option is C addition, subtraction and multiplication
Division of rational number that can be expressed as terminating decimal may not be rational. $∴$ $D$ is closed under addition, subtraction, and multiplication.