The set of natural numbers is closed under the binary operations of

addition, subtraction, multiplication and division.

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addition, subtraction, multiplication but not division.

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addition and multiplication but not subtraction and division.

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addition and subtraction but not multiplication and division.

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Solution

The correct option is D addition and multiplication but not subtraction and division.
The sum and difference of any two natural numbers is also a natural number.
But, the difference or ratio of two natural numbers need not always be a natural number.
Therefore, the set of natural numbers is closed under the binary operations of addition and multiplication but not under subtraction and division.

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