Which of the following sets is closed under multiplication?

{0, 1, 2, 4}

{0, 1}

{1, 2}

None of the sets are closed under multiplication.

Question

Which of the following sets is closed under multiplication?


		
{0, 1, 2, 4}
		
{0, 1}
		
{1, 2}
		
None of the sets are closed under multiplication.

mathmate · Answer

A set is closed under multiplication if we take any two numbers out of the set and multiply, the result is a member of the set.  The two numbers may be repeated, i.e. multiply by itself.

For example:
X={0,-1}
is not closed because 0*0=0 $\in$ X, 0*(-1)=0 $\in$ X, but (-1)*(-1)=1 $\notin$ X, so
X is not closed under multiplication.

You can repeat the same test for all the given sets to get your answer.