Question 1 :
If $n(A) = 65, n(B) = 32$ and $\displaystyle n\left ( A\cap B \right )=14 $, then $\displaystyle n\left ( A\Delta  B \right ) $ equals

Question 2 :
The value of c for which the set {(x, y) | $\displaystyle x^{2}+y^{2}+2x\leq 1$} $\displaystyle \cap $ {$(x, y) | x - y + c$ $\displaystyle \geq 0 $} contains only one point in common is

Question 3 :
Let $A$ and $B$ be two sets such that $A\cap B=\phi$. Find the value of $(A\cup B')=$

Question 4 :
<p>Suppose ${ A }_{ 1 },{ A }_{ 2 },...,{ A }_{ 30 }$ are thirty sets, each with five elements and ${ B }_{ 1 },{ B }_{ 2 },...,{ B }_{ 30 }$ are $n$ sets ecah with three elements. Let $\displaystyle&#160;\bigcup _{ i=1 }^{ 30 }{ { A }_{ i }= } \bigcup _{ j=1 }^{ n }{ { B }_{ j } } =S$</p><p>If each element of $S$ belongs to exactly ten of the ${ A }_{ i }'s$ and exactly none of the ${ B }_{ j }'s$ then $n=$</p>

Question 5 :
Set $A$ has $3$ elements and set $B$ has $6$ elements.&#160;What can be the minimum number of elements in $A\cup B$?

Question 6 :
If $A=\left\{2, 4, 6, 8, 10\right\}, B=\left\{1, 3, 5, 7, 9\right\}$, then $A-B$ =____________

Question 7 :
If $A, B$ and $C$ are any three set, then $A \cup (B\cap C) =$<div><br/></div>

Question 10 :
Let $A$ and $B$ have $3$ and $6$ elements respectively. What can be the minimum number of elements in $A\cup B$?

Question 11 :
If A and B be two sets containing $4$ and $8$ elements respectively, what can be the maximum number of elements in $A\cup B$? Find also, the minimum number of elements in $(A\cup B)$?

Question 12 :
Given the set $S$ whose elements are zero and the even integers, positive and negative. Of the five operations applied to any pair of elements : $(1)$ addition $(2)$ subtraction $(3)$ multiplication $(4)$ division $(5)$ finding the arithmetic mean (average), those operations that yield only elements of $S$ are

Question 13 :
If $n(A)$ denotes the number of elements in set A and if $n(A)=4, n(B)=5$ and $n(A\cap B)=3$ then $n\left[ \left( A\times B \right) \cap \left( B\times A \right)&nbsp; \right] =$

Question 14 :
For two sets $A$ and $B$, $ A\cap \left( A\cup B \right)=$

Question 15 :
If X $=$ (multiples of 2), Y $=$ (multiples of 5), Z $=$ (multiples of 10), then $X \cap&nbsp; ( Y \cap&nbsp; Z )$ is equal to<br>

Question 16 :
Let $U=\left\{ 1,2,3,4,5,6,7,8,9,10 \right\}$, $A=\left\{ 1,2,5 \right\}$, $B=\left\{ 6,7 \right\}$ then $A\cap B'$ is

Question 17 :
Let $A_1, A_2$ and $A_3$ be subsets of a set $X$. Which one of the following is correct?

Question 18 :
Let A and B be two non empty subsets of a set X If&#160;$\displaystyle \left ( &#160;A-B\right )\cup \left ( B-A \right )=A\cup B $, then which one of the following is correct?

Question 20 :
Let $A$ and $B$ be two sets in the universal set. Then $ (A \cup B)'$ equals

Question 22 :
Let $P = \{ x | x$ is a multiple of $3$ and less than $100 $ ,$x$ $\displaystyle \in $ $N \}$<br/>$Q = \{ x | x$ is a multiple of $10$ and less than $100$, $x$ $\displaystyle \in$ $N\}$<br/>

Question 23 :
Let $A$ and $B$ have $3$ and $6$ elements respectively. The minimum number of elements in $A\cup B$

Question 24 :
If $X = \left \{1, 2, 3, ..., 10\right \}$ and $A = \left \{1, 2, 3, 4, 5\right \}$. Then, the number of subsets $B$ of $X$ such that $A - B = \left \{4\right \}$ is

Question 25 :
If $A, B$ be any two sets, then $\displaystyle \left( A \cup &#160;B \right) '$&#160;is equal to

Question 26 :
Let $\displaystyle A=\left \{ \left ( x,y \right )\ni y=e^{2x} \forall x\in R\right \}$&nbsp; $ \displaystyle B=\left \{ \left ( x,y \right )\ni y=e^{-2x} \forall x\in R\right \}$ then <br>

Question 28 :
If $A_{1}, A_{2},..., A_{100}$ are sets such that $n(A_{i}) = i + 2,$&nbsp;$A_{1}\subset A_{2}\subset A_{3}........A_{100}$ and $\bigcap_{i=3}^{100}A_{i}=A,$ then&nbsp;$n(A)=$<br>

Question 29 :
$A = \{1,2,4\}, B = \{2, 4,5\}, C = \{2, 5\}, $then $(A - B) \cup (B- C)$ is

Question 30 :
If&#160;$A=\left \{ \left ( x, y \right )\mid x^{2}+y^{2}\leq 4 \right \}$ and $B=\left \{ \left ( x, y \right )\mid \left ( x-3 \right )^{2}+y^{2}\leq 4 \right \}$ and the point $\displaystyle P\left ( a, a-\frac{1}{2} \right )$ belongs to the set $B-A$, then the set of possible real values of $a$ is: