If $A$ and $B$ are two sets then $(A -B) \cup (B -A) \cup (A \cap B)$ is equal to

If $X$ and $Y$ are two sets such that $X \cup Y$ has $18$ elements, $X$ has $8$ elements and $Y$ has $15$ elements ; how many elements does $X \cap Y$ have?

State whether each of the following statement is true or false. Justify you answer.

$\{2,3,4,5\}$ and $\{3,6\}$ are disjoint sets.

If $A = \{ x:x$ is a natural number $\} ,B = \{ x:x$ is an even natural number $\} $ $C = \{ x:x$ is an odd natural number $\} $ and $D = \{ x:x$ is a prime number $\} ,$ find

$C \cap D$

If $A, B, C$ be three sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$, then

Using that for any sets $\mathrm{A}$ and $\mathrm{B},$

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