Operations on Sets

If $A=\left\{x:x N, x \text{is divisible by} 2\right\}$, $B=\left\{x:x^2-3x+2=0\right\}$ find $A\cap B$.

Find which are/ is the statement (s) false about complement of a set?

$a.$ The set and its complement are always universal sets.

$b.$ The complement of a universal set is the empty set.

$c.$ The complement of the empty set is a universal set.

State De Morgan's Law and then prove the statement.

Let $U$ be the universal set for $A$ and $B$, where $B$ is complement set of $A$.

If $n\left(A\right)=4$ and $n\left(U\right)=11$ then find $n\left(B\right)$

According to Idempotent property of intersection of sets, for any set $P$, $P\cap P$ is 

State and prove Idempotent property of intersection of sets.

Prove the associative property of union of sets $A=\left\{2,5\right\}$, $B=\left\{5,8\right\}$ and $C=\left\{4,6\right\}$.

Explain the existence of identity for union of sets.

Which of the following is not equal to set $A$?

Which of the following is equal to $A\cup A\text{'}$?

If $A=\left\{1, 2, 3, 4\right\}$, $B=\left\{-2, 3, 4, 5, 6\right\}$ and $C=\left\{2, 4, 5, 6, 7\right\}$.

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

If $A=\left\{x: -3\le x<4, x\in Z\right\}$, $B=\left\{x: x<5, x\in N\right\}$ and $C=\left\{-5, -3, -1, 0, 1, 3\right\}$

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

If $A=\left\{3, 5, 12\right\}$, $B=\left\{9, 11\right\}$ and $C=\left\{2, 11, 15\right\}$

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

If $A=\left\{0, 1, 2, 3, 4\right\}$, $B=\left\{1, -2, 3, 4, 5, 6\right\}$ and $C=\left\{2, 4, 6, 7\right\}$.

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

If $A=\left\{3, 5, 9\right\}$, $B=\left\{9, 11, 15\right\}$ and $C=\left\{2, 11, 9\right\}$

Then, $\left(A\cap B\right)\cap C=A\cap \left(B\cap C\right)$

Explain the operation of intersection of sets is associative with the example.

The operation of intersection of sets is commutative.

If $A=\left\{3, 5, 9\right\}$, $B=\left\{9, 11, 15\right\}$ and $C=\left\{2, 11, 15, 16\right\}$

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

$A=\left\{m,n\right\}$ and $B=\left\{x,y\right\}$. Find $A\cup B$.

$A=\left\{p,q\right\}$ and $B=\left\{r,s\right\}$. Find $A\cup B$.