Which of the following gives an example of a set that is closed under multiplication? choose all that apply.. . a. the product of a perfect cube and a perfect cube. b. the product of 0 and 0. c. the product of a whole number and a whole number. d. the product of a perfect square and a perfect square. i think its b and c?

The correct answer is:

Option: A , Option: B , Option: C , Option: D

For a set to be closed under multiplication means if two elements are taken from that set then their multiplication must also belong to the same set.

A)

The product of a perfect cube and a perfect cube.

Let a be a perfect cube of "m"

and b be a perfect cube of "n"

i.e.

Hence,

i.e.

Hence, this set if closed under multiplication.

B)

The product of 0 and 0.

when we take the product of 0 and 0 then the resultant is also zero.

Hence, this set  is also closed under multiplication.

C)

The product of a whole number and a whole number.

When we multiply a whole number to a whole number then the product is again a whole number.

This set is also closed under multiplication.

D)

The product of a perfect square and a perfect square.

Let us take two elements of the set as x and y

i.e.

and

Hence,

i.e.

Hence, the set is closed under multiplication.

no, because the sides are not congruent