If $U=\left\{1,2,3,4,5,6,7,8,9\right\}$, $A=\left\{2,4,6,8\right\}$, and $B=\left\{2,3,5,7\right\}$ verify that:

$(A \cap B)’ = (A’ \cup B’)$

Let $A=\left\{a,b,c\right\}, B=\left\{b,c,d,e\right\}$ and $C=\left\{c,d,e,f\right\}$ be subsets of $U=\left\{a,b,c,d,e,f\right\}$. Then verify that: 

$(A’)’ = A$

Let $A=\left\{a,b,c\right\}, B=\left\{b,c,d,e\right\}$ and $C=\left\{c,d,e,f\right\}$ be subsets of $U=\left\{a,b,c,d,e,f\right\}$. Then verify that: 

$(A\cup B)’ =\left( A\text{'}\cap B\text{'}\right)$

Let $A=\left\{a,b,c\right\}, B=\left\{b,c,d,e\right\}$ and $C=\left\{c,d,e,f\right\}$ be subsets of $U=\left\{a,b,c,d,e,f\right\}$. Then verify that: 

$(A\cap B)’ =\left( A\text{'}\cup B\text{'}\right)$

For any sets $A$ and $B$, prove that:

$(A – B) \cap B = \varphi$

For any sets $A$ and $B$, prove that: $A \cup (B – A) = A \cup B$

For any sets $A$ and $B$, prove that:

$(A – B) \cup (A \cap B) = A$

For any sets $A$ and $B$, prove that:

$(A \cup B) – B = A – B$