Venn Diagram Operations on Sets

If $A=\left\{1,5,4,7,9\right\}$ and $B=\left\{5,3,7,8,9\right\}$ then draw Venn diagram for symmetric difference for $A$ and $B$.

If $A=\left\{1,2,4,7,9\right\}$ and $B=\left\{2,3,7,8,9\right\}$ then draw Venn diagram for symmetric difference for $A$ and $B$.

Verify the associative property of union of sets for the following.

$A=\left\{1,2,3,4\right\}, B=\left\{2,3,4,5\right\}$and $C=\left\{3,4,5,6\right\}$ 

Verify the commutative property of union of sets for the following.

$A=\left\{1,2,3,4\right\}$ and $B=\left\{3,4,5\right\}$

Verify the idempotent property of sets of union for the set $A=\left\{1,2,3\right\}$

State and prove Idempotent property of intersection of sets.

Explain the existence of identity for union of sets.

By giving one example show that Union operation in sets follows commutative law.

$A=\left\{a,b\right\}$, $B=\left\{e,f\right\}$. Verify closure property of union of two sets.

$A=\left\{a,b,c\right\}$, $B=\left\{d,e,f\right\}$. Verify closure property of union of two sets.

$A=\left\{1,2,3\right\}$, $B=\left\{2,3,4,5\right\}$. Verify closure property of union of two sets.

$A=\left\{1,2,3,4\right\}$, $B=\left\{2,3,4,5,6\right\}$. Verify closure property of union of two sets.

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Verify closure property of union of two sets.

$A=\left\{1,2,3\right\}$ and $U=\left\{1,2,3,4\right\}$. Find $A\cap U$.

$A=\left\{1,4\right\}$ and $U=\left\{1,2,3,4\right\}$. Find $A\cap U$.

$A=\left\{2,4\right\}$ and $U=\left\{1,2,3,4\right\}$. Find $A\cap U$.

$A=\left\{1,3\right\}$ and $U=\left\{1,2,3,4\right\}$. Find $A\cap U$.

$A=\left\{1,2\right\}$ and $U=\left\{1,2,3,4\right\}$. Find $A\cap U$.

If $A=\left\{\mathrm{prime} \mathrm{numbers} \mathrm{from} 10 \mathrm{to} 25\right\}$ and $B=\left\{\mathrm{odd} \mathrm{numbers} \mathrm{from} 10 \mathrm{to} 25\right\}$. Prove that, $A\cap B$ belongs to set of numbers under $25$.

If $A=\left\{\mathrm{prime} \mathrm{numbers} \mathrm{under} 25\right\}$ and $\mathrm{B}=\left\{\mathrm{odd} \mathrm{numbers} \mathrm{under} 25\right\}$. Prove that, $A\cap B$ belongs to set of numbers under $25$.