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...

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.

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lidaralbany lidaralbany · Answer 2 · 2019-07-25T06:58:36+02:00

Answer:

The correct answer is:

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

Step-by-step 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.

[tex]a=m^3\\\\and\\\\b=n^3[/tex]

Hence,

[tex]a\cdot b=m^3\cdot n^3\\\\i.e.\\\\a\cdot b=(mn)^3[/tex]

i.e.

[tex]a\cdot b\ \text{is a perfect cube of mn}[/tex]

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.

[tex]x=a^2[/tex]

and

[tex]y=b^2[/tex]

Hence,

[tex]x\cdot y=a^2\cdot b^2\\\\i.e.\\\\x\cdot y=(ab)^2[/tex]

i.e.

[tex]x\cdot y\ \text{is\ also\ a perfect\ square}[/tex]

Hence, the set is closed under multiplication.