The union of X and Y contains all elements that are in X and Y. Notice that we do not count an element twice if it exists in both sets. First, we need to rewrite X as a set of all integers that are odd and less than 16.
X&={x | x is an odd whole number less than 16}
X&={1,3,5,7,9,11,13,15}
Now we can find the union of those two sets.
X&={1,3,5,7, 9,11,13,15}
Y&={2,6,9,10,16}
X⋃ Y & ={1,2,3,5,6,7,9,10,11,13,15,16}
Knowing X⋃ Y, we can find the union of X⋃ Y and Z. This will give us X⋃ Y⋃ Z. To do this, we start by rewriting Z as a set of all integers that are even and less than 19.
Z&={x | x is an even whole number less than19}
Z&={0,2,4,6,8,10,12,14,16,18}
The union of X⋃ Y and Z contains all elements that are in X⋃ Y and Z. Again, we do not count an element twice if it exists in both sets.
Z & ={0, 2,4, 6,8, 10,12,14, 16,18}
X⋃ Y & ={1,2,3,5,6,7,9,10,11,13,15,16}
X⋃ Y⋃ Z & = {0,1,2,3,4,5,6,7,8,9,10, & 11,12,13,14,15,16,18}.
