Prove that $\overline { A \cap B } = \bar { A } \cup \bar { B }$ by giving a containment proof (that is, prove that the left side is a subset of the right side and that the right side is a subset of the left side).

Question

Quizplus · Accepted Answer

The Answer is

A \cap ( B \cup C ) \subseteq ( A \cap B ) \cup ( A \cap C )

Let

x \in A \cap ( B \cup C ) , \quad herefore x \in A

and

x \in B \cup C , herefore x \in A

and

x \in B , ext { or } x \in A

and

x \in C , herefore x \in ( A \cap B ) \cup ( A \cap C )

Reversing the steps gives the opposite containment.

Prove That A∩B‾=Aˉ∪Bˉ\overline { A \cap B } = \bar { A } \cup \bar { B }A∩B=Aˉ∪Bˉ

Prove That $\overline { A \cap B } = \bar { A } \cup \bar { B }$