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

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addition, subtraction and division.

addition, multiplication and division.

addition, subtraction and multiplication.

subtraction, multiplication and division.

answer is C.

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Detailed Solution

Given that, D be subset of the set of all rational numbers, which can be expressed as terminating decimals.
We know that,
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.
Hence, D is closed under addition, subtraction and multiplication.
So, the answer is option 3.

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