Properties of Intersection of Sets

Q. For any three sets $X,Y\&Z,X\cap (Y\cap Z)$ is equal to

1. $(X\cap Y)\cap Z$
2. $(Y\cap X)\cap Z$
3. $Y\cap (X\cap Z)$
4. $Y\cap (Z\cap X)$

Q. Consider the following statements :
$1.N\cup (B\cap Z)=(N\cup B)\cap Z$ for any subset $B$ of $R,$ where $N$ is the set of positive integers, $Z$ is the set of integers, $R$ is the set of real numbers.

$2.$ Let $A=\{n\in N:1\le n\le 24,n\text{is a multiple of}3\}.$ There exists no subset $B$ of $N$ such that the number of elements in $A$ is equal to the number of elements in $B.$

Which of the above statements is/are correct?

1. $1$ only
2. $2$ only
3. Both $1$ and $2$
4. Neither $1$ nor \(2\
   )

Q. $\text{For any two sets}A\&B\text{if}$
$A\subset B,\text{then}A\cap B=$

1. $A$
2. $B$
3. $A\cup B$

Q. For three sets $A,B\&C$ if $A\cap B=\varnothing ,$ then $A\cap (B\cup C)=$

1. $\varnothing$
2. $B\cap C$
3. $A\cap C$
4. $A\cup C$

Q. For any set $A,A\cap A=A.$

1. False
2. True

Q. Associative Property for three sets $A,B,\&C$ states $A\cap (B\cap C)=$

1. $(A\cap B)\cap C$
2. $(A\cap B)\cup C$
3. $(A\cup B)\cup C$

Q. For any two sets $A\&B;A\cap B=$

1. $B\cap A$
2. $B$
3. $A\cup B$

Q. The set $(A\cup B\cup C)\cap (A\cap B^{\prime }\cap C^{\prime })\cap C^{\prime }$ is equal to

1. $B\cap C^{\prime }$
2. $A\cap C$
3. $B^{\prime }\cap C^{\prime }$
4. None of these

Q. Two sets given such that $A=\{a:a\text{is a prime number}<25\}\&$
$B=\{b:b\in N,10\le b\le 18\},$ the select the correct statements.

1. $A\cap B=\{11,13,17\}$
2. $A\cup B=B\cup A$
3. $A\cap B=B\cap A$
4. $A\subset B$

Q. Consider the following statements :
$1.N\cup (B\cap Z)=(N\cup B)\cap Z$ for any subset $B$ of $R,$ where $N$ is the set of positive integers, $Z$ is the set of integers, $R$ is the set of real numbers.

$2.$ Let $A=\{n\in N:1\le n\le 24,n\text{is a multiple of}3\}.$ There exists no subset $B$ of $N$ such that the number of elements in $A$ is equal to the number of elements in $B.$

Which of the above statements is/are correct?

1. $1$ only
2. $2$ only
3. Both $1$ and $2$
4. Neither $1$ nor \(2\
   )

Q. For three sets $A,B\&C,$ if $A\subset B,A\subset C$ then $A\cap (B\cup C)=$

1. $A$
2. $B\cap C$
3. $B\cup C$

Q.

If X and Y are two sets and $X^{\prime }$ denotes the complement of X, then
$X\cap (X\cup Y{)}^{\prime }$ is equal to

1. X

2. Y

3. $\varphi$

4. $X\cap Y$