Positive and negative integers together are closed under ............

addition and subtraction

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addition and multiplication

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multiplication and division

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multiplication

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Solution

The correct option is C multiplication
The set of positive and negative integers does not include $0$ . Now, addition of two integers may result in $0.$
Eg : $- 1 + 1 = 0$
And subtraction of two integers may also result in $0.$
Eg : $- 1 - (- 1) = - 1 + 1 = 0.$
And we also know that integers are not closed under division. Also, when two non-zero numbers are multiplied, the product is a non-zero integer.

Suggest Corrections

Column-I	Column-II
(i) For any two integers a and b, a $\times b$ is also an integer. Thus, integers are	(a) Distributive under addition and multiplication
(ii) $a \times b = b \times a$ ; denotes that integers are	(b) Positive quotient
(iii) $a \times (b + c) = a \times b + a \times c;$ this denotes that integers are	(c) Closed under multiplication
(iv) The division of a negative integer by another negative integer results in	(d) Commutative under multipication