Your characteristics of each set are:
Z: A set of integers. So natural numbers with a sign (negative and positive) and zero. eg. -x, 0, x
Q: A set of rational numbers. A rational number is a division of two integers like 3/5
So Z ∪ Q = { 16 , -8 , 0 , -1/9 , 6.4 , 2 , sqrt(2.89) } if
Z = {16, -8, 0, 2} and
Q = {64/4, -8, 0, -1/9, 6.4, sqrt(4), sqrt(2.89)}
{ 64/4 , -8 , 0 , -1/9 , 6.4 , square root(4) , square root(-9) , square root(2.89) , cube root(144) } = Z ∪ Q ∪ R
With R being a set of real numbers R = {64/4 , -8 , 0 , -1/9 , 6.4 , square root(4) , square root(-9) , square root(2.89) , cube root(144)}