Let $A=\left\{a,b,c,e,f\right\}, B=\left\{c,d,e,g\right\}$ and $C=\left\{b,c,f,g\right\}$ be subsets of the set $U=\left\{a,b,c,d,e,f,g,h\right\}$.

Draw Venn diagrams to represent the following set: $(B-C)\cup (C-B)$

Let $A=\left\{a,e,i,o,u\right\}, B=\left\{a,d,e,o,v\right\}$ and $C=\left\{e,o,t,m\right\}$. Using Venn diagrams, verify the following:

$A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$

Let $A=\left\{a,e,i,o,u\right\}, B=\left\{a,d,e,o,v\right\}$ and $C=\left\{e,o,t,m\right\}$. Using Venn diagrams, verify the following:

$A\cap (B\cup C) = (A\cap B)\cup (A\cap C)$

Let $A=\left\{2,3,5,7,11,13\right\}, B=\left\{5,7,9,11,15\right\}$ be subsets of $U=\left\{2,3,5,7,9,11,13,15\right\}$. Using Venn diagrams, verify that:

${(A\cup B)}^{\text{'}}=(A^{\text{'}}\cap B^{\text{'}})$

Let $A=\left\{2,3,5,7,11,13\right\}, B=\left\{5,7,9,11,15\right\}$ be subsets of $U=\left\{2,3,5,7,9,11,13,15\right\}$. Using Venn diagrams, verify that:

${(A\cap B)}^{\text{'}}=(A^{\text{'}}\cup B^{\text{'}})$