User:Practex baidukai

Prove that

$$ (A \cap V)^c = A^c \cup B^c. $$

Proof:

Suppose that $$x \in (A \cap B)^c. $$ Then $$x \notin A \cap B, $$ so that $$x \notin A or x \notin B. $$ This is equivalent to $$x \notin A \cup B, or x \in A^c \cup B^c. $$

Therefore, $$(A \cup B)^c \sube A^c \cup B^c. $$