Properties of Operations on Sets

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

Verify distributive property of intersection over union for the sets $A=\left\{1,4,7,8,9\right\}; B=\left\{1,3,5,7,9\right\}; C=\left\{0,2,5,8,9\right\}$

Universal Set $\mathrm{U}=\left\{1,2,3,4,5,6,7,8,9,10\right\}$

Set $\mathrm{A}=\left\{1,2,3,5,7\right\}$

Find the set that representing $\left(\mathrm{A}\cap \mathrm{U}\right)$.

$A,B$ are the independent sets, the intersection of $A$ and $B$ gives the universal set.

Null set is an identity element for the Intersection operation.

Check whether the intersection of two sets is Associative or not by taking an example.

Check whether the intersection of two sets is commutative or not.

Verify idempotent property of sets over intersection for the set $A=\left\{1,4,7,8,9\right\}$

For the finite sets $A,B$. The intersection of the sets $A\cap B=B\cap A$

Verify that the union of any set with a universal set gives the universal set or not for the sets given below.

Set $A=\left\{2,3,5,7\right\}$, 

Universal set $U=\left\{1,2,3,4,5,6,7,8,10\right\}$

The union of a set and any other set will never give a 

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

Write about the commutative property of sets of union. 

The union of any set $B$ with itself gives the set $B$

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

If $A=\left\{1,2\right\}$ and $B=\left\{2,4\right\}$, then verify that $A\cap B=B\cap A$.

If $A=\left\{1,2\right\}$ and $B=\left\{2,4\right\}$, then verify that $A\cup B=B\cup A$.

If $A=\left\{1,3,7\right\}$ and $B=\left\{1,3\right\}$, then verify that $A\cap B=B\cap A$.

If $A=\left\{1,3,7\right\}$ and $B=\left\{1,3\right\}$, then verify that $A\cup B=B\cup A$.

Let $A=\{b,d,e,g,h\}\text{ and }B=\{a,e,c,h\}$, then verify that, $n(A-B)=n\left(A\right)-n(A\cap B)$.