Start with the universal set U
U = {q, r, s, t, u, v, w, x, y, z}
Cross off anything you find in set A = {q, s, u, w, y}
U = {q, r, s, t, u, v, w, x, y, z}
U \ A = {q, r, s, t, u, v, w, x, y, z} blue items are crossed off the list
U \ A = {r, t, v, x z}
A ' = {r, t, v, x, z}
The notation U \ A tells the reader to "start with set U and kick out the items in set A", which is what a complement set is. We write A', or A prime, to indicate a complement set to set A.
Then union this with the items in set B.
A' U B = {r, t, v, x, z} U {q, s, y, z}
A' U B = {r, t, v, x, z, q, s, y, z}
A' U B = {q, r, s, t, v, x, y, z}
Notice I sorted alphabetically and tossed out the duplicates
The union of two sets is the result of combining the two sets together. Almost like we're dumping the two smaller sets A' and B into one larger bin.