R S Aggarwal Solutions for Exercise 6: EXERCISE 1F

Let $A=\left\{2,4,6,8,10\right\}, B=\left\{4,8,12,16\right\}$ and $C=\left\{6,12,18,24\right\}$. Using Venn diagrams, verify that: $(A\cup B)\cup C=A\cup (B\cup C)$

Let $A=\left\{2,4,6,8,10\right\}, B=\left\{4,8,12,16\right\}$ and $C=\left\{6,12,18,24\right\}$. Using Venn diagrams, verify that:
$(A\cap B)\cap C = A\cap (B\cap C)$

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:

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

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 $A \subset B \subset C$. Exhibit it in a Venn diagram.
 

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:

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

Using Venn diagrams, show that $(A – B), (A \cap B)$ and $(B – A)$ are disjoint sets,taking $A=\left\{2,4,6,8,10,12\right\}$ and $B=\left\{3,6,9,12,15,\right\}$.