Question

Which set is closed under the operation multiplication?

A.
{0, 1, 2}


B.
{1, 2}


C.
{1}


D.
{1, 2, 3}

Answer 1

Your answer is -
B.
{1, 2}

Answer 2

For a set to be closed, if you multiply 2 of the numbers in the set, the number is in the set.

This dosent work for A since 2*2 = 4 and 4 isnt in the set
Same for B

C is closed as 1*1 = 1

D isnt closed as 3*3 = 9

Hence C is the correct answer.

To add a proper example.

the set {-1, 0, 1} is also closed, because
-1*-1 = 1 which is in the set
-1*0 = 0 which is in the set
-1*1 = -1 which is in the set
0*x = 0 which is in the set
And i think you understand the rest :)