# Math Help - Venn Diagram

1. ## Venn Diagram

(A U B) U Cc what will be its venn diagram?????

(A U B) U Cc what will be its venn diagram?????
Since it's all UNION, you could literally add/shade the 3 areas (A, B, compliment of C).

$A \cup B \cup C\:\!'$

What will be its Venn diagram?

Let: . $S \;=\;A \cup B \cup C\:\!'$

Take the complement of both sides: . $S\:\!' \;=\;\bigg[A \cup B \cup C\:\!'\bigg]\:\!'$

. . DeMorgan's Law gives us: . $S\:\!' \;=\;A' \cap B\:\!' \cap C$

We have: . $S$-complement is the region not in $A$, not in $B$, and in $C.$
. . That is, that region which is in $C$ only. .(Visualize that region.)

Then $S$ is everything but that region.