Cardinal Properties of Sets

The number of elements in set $A$ is $30$, the number of elements in the intersection of the sets $A,B$ is $25$. Find the cardinal number of the difference of the two sets $A,B$.

The number of elements in set $A$ is $40$, the number of elements in the intersection of the sets $A,B$ is $25$. Find the number of Elements in the difference of two sets $A,B$.

In the sets $A,B$, the number of elements in set $A$ is $20$, the number of elements in set $B$ is $30$, the number of elements in the union of both sets $A,B$ is $40$. Find the number of elements at the intersection of two sets $A,B$. 

$A,B$ are two disjoint sets. $A$ has $6$ elements, $B$ has $4$ elements. Find the number of elements in $\left(A\cup B\right)$. 

If $X$ and $Y$ are two sets such that $X\cup Y$ has $50$ elements, $X$ has $28$ elements and $Y$ has $32$ elements, how many elements does $X\cap Y$ have ?

In a survey of $500$ students in a school, $150$ were listed as taking apple juice, $200$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

Let $A=\{3,6,12,15,18,21\},B=\{4,8,12,16,20\},C=\{2,4,6,8,10,12,14,16\}$ and  $D=\{5,10,15,20\}$. Find

$D-C$

In a joint family of $15$ persons, $9$ take tea, $8$ take milk and $2$ take neither. How many members take both tea and milk?