Hello, Discrete!
Here's another proof . . .
Prove: .
We need (among other definitions and properties):
. . [1] . . (Def. of set subtraction)
. . [2] .
. . [3] .
We have: .
. . . . . . . . . . . . . . . . . . . . [1]
. . . . . . . . . . . . . . . . DeMorgan's Law
. . . . . . . Distributive Property
. . . . . . . . . . . . . . . . . . . . [2]
. . . . . . . . . . . . . . . . . . . . . . . . . . . [3]
. . . . . . . . . . . . . . . . . . . . . . . . . . . [1]