Question

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? help anyone...

Answer 1

The correct answer is:

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

Explanation:

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.

`a=m^3\\\\and\\\\b=n^3`

Hence,

`a\cdot b=m^3\cdot n^3\\\\i.e.\\\\a\cdot b=(mn)^3`

i.e.

`a\cdot b\ \text{is a perfect cube of mn}`

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.

`x=a^2`

and

`y=b^2`

Hence,

`x\cdot y=a^2\cdot b^2\\\\i.e.\\\\x\cdot y=(ab)^2`

i.e.

`x\cdot y\ \text{is\ also\ a perfect\ square}`

Hence, the set is closed under multiplication.

Answer 2

All the four choices that are given in the question can be considered as as examples of a set that is closed under multiplication. The correct options among all the options that are given in the question are options "A", "B", "C" and "D". I hope that the answer has come to your help.