First, you need to draw the venn diagram for the elements of X and Y. Notice that Y is a proper subset of X.

Proper Subset means that all elements of Y are elements of X but not all element are X are elements of Y. In simple English it means that all elements in Y is also found in X but X has some extra elements that Y does not have.

Then ( this is where it get tricky) you need to find a elements that satisfy Y U(union) Z = X and n(Z)=5.

What this means is that the elements of Y combine with Z is the same as the elements in X. And there is a total of 5 elements in Z (n(Z)=5).

You have to do trail and error to find the answers. Use a pencil and  circle the elements , keep on trying  until you think it will satisfy both conditions. Unfortunately there is no mathematical formula for set notation.

 

Z = { 2,4,6,8,10}

 

Z = { 2,4,6,10,12}

 

Z = { 2,6,8,10,12}

 

You do not need to list all three . The question is only asking for one of the three ("find a set Z").