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.
The sum, difference or product of two rational numbers will be a number that can be expressed as a terminating decimal.
The ratio of two rational numbers need not be always expressible as a terminating decimal.
So, the answer is option C.

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Similar questions

Q. 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:

Q. Question 77
Rational numbers are closed under addition and multiplication but not under subtraction.

Q. 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.

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.

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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