Intersection of Sets

Q.

Let, ${\cup }_{i=1}^{50}{X}_i={\cup }_{i=1}^n{Y}_i=T_{}$

where each $X_i$ contains $10$ elements and each $Y_i$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_i’s$ and exactly $6$ of sets $Y_i’s$, then $n$ is equal to :

1. $15$

2. $30$

3. $50$

4. $45$

Q.

If $n\left(A\right)=3,n\left(B\right)=6$ and $A\subseteq B$. Then the number of elements in $A\cup B$ is equal to.

$3$

$9$

$6$

None of these.

Q.

The cardinality of the set $P\left\{P\right[P(\varnothing )\left]\right\}$ is

1. $0$

2. $1$

3. $2$

4. $4$

Q.

Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injections that can be defined from $A$ to $B$ is:

1. $144$

2. $12$

3. $24$

4. $64$

Q.

If $12500=5^a\times 2^b$, Find $a$ and $b$.

Q.

If $X$ and $Y$ are two sets such that $(X\cup Y)$ has $60$ elements, $X$ has $38$ elements and $Y$ has $42$ elements, how many elements do $(X\cap Y)$ have?

1. $11$

2. $20$

3. $13$

4. None of these

Q.

If $N_a=\{an:n\in N\}$ , then $N_3\cap N_4$ =

1. $N_7$

2. $N_{12}$

3. $N_3$

4. $N_4$

Q. If the sets A and B are defined as
$A=\{x:x=2n,n\in N,n<100\}B=\{x:x=3n,n\in N,n<100\}$
then, the number of elements in $A\cap B$ is

1. 16
2. 198
3. 33
4. 59

Q. If $A$ is the set of the divisors of $15,B$ is the set of prime numbers less than $10$ and $C$ is the set of even natural numbers smaller than $9,$ then $(A\cup C)\cap B$ is the set

1. $\{1,3,5\}$
2. $\{1,2,3\}$
3. $\{2,3,5\}$
4. $\{2,5\}$

Q. If $A,B,C$ and $D$ be four sets such that $A=\{2,4,6,8,10,12\},B=\{3,6,9,12,15\}$, $C=\{1,4,7,10,13,16\}$ and $D=\{x:x\in N\}$, then the number of elements in $\left[\right(A\cup B)\cup C]\cap D$ is

Q. If $A=\left\{\right(x,y):x^2+y^2\le 1;x,y\in R\}$ and $B=\left\{\right(x,y):x^2+y^2\ge 4;x,y\in R\}$, then

1. $A-B=\varphi$
2. $B-A=\varphi$
3. $A\cap B\ne \varphi$
4. $A\cap B=\varphi$

Q. $A$ and $B$ are two sets such that
$A$ = Set of all prime numbers and
$B$ = Set of all even natural numbers,
then find $A\cap B.$

1. $2$
2. $\varphi$
3. (a) and (b) above.
4. None of the above

Q. Let $A=\{x:x\text{is a prime factor of}240\}$ and $B=\{y:y\text{is the sum of any two prime factors of}240\}$. Then which of the following options is true?

1. $5\notin A\cap B$
2. $7\in A\cap B$
3. $8\in A\cap B$
4. $8\in A\cup B$

Q.

$\text{If}A=x:x\text{is a prime number}B=x:x\text{is an odd natural number},\text{then}A\cap B\text{is}$

1. {1, 3, 5, 7, 11, 13, 17, .....}

2. {2, 3, 5, 7, 9, 11, .....}

3. {3, 5, 7, 11, 13, 17, .....}

4. {1, 2, 3, 5, 7, 9, 11, .....}

Q. Let $A,B,C$ are three sets such that

Then $A^C\cap B\cap C^C=$

1. $\left\{8\right\}$
2. $\left\{6\right\}$
3. $\{6,8\}$
4. $\{3,6,8\}$

Q. If $A=\{x:x^2-5x+6=0\},B=\{2,4\},C=\{4,5\}$, then $A\times (B\cap C)$ is

1. $\left\{\right(2,4),(3,4\left)\right\}$
2. $\left\{\right(4,2),(4,3\left)\right\}$
3. $\left\{\right(2,4),(3,4),(4,4\left)\right\}$
4. $\left\{\right(1,2\left)\right\}$

Q. If $X=\{x:x=8^n-7n-1,n\in N\}$ and $Y=\{y:y=49n-49,n\in N\},$ then which of the following is (are) TRUE?

1. $X\subset Y$
2. $Y\subset X$
3. $X\cap Y=X$
4. $X\cap Y=Y$

Q. Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can formed such that $Y\subseteq X,Z\subseteq XandY\cap Z$ is empty is:

1. $5^2$
2. $3^5$
3. $2^5$
4. $5^3$

Q.

$\text{If}A=x:x\text{is a prime number}B=x:x\text{is an odd natural number},\text{then}A\cap B\text{is}$

1. {1, 3, 5, 7, 11, 13, 17, .....}

2. {2, 3, 5, 7, 9, 11, .....}

3. {3, 5, 7, 11, 13, 17, .....}

4. {1, 2, 3, 5, 7, 9, 11, .....}

Q. Let $A=\{x:x\text{is a natural number and a factor of}18\}$ and
$B=\{x:x\text{is a natural number and less than 6}\}$.
If $A\cap B=\{a,b,c\}$, then the value of $a+b+c$ is

Q. If $A,B$ and $C$ are three subsets of a non-empty set $X$, then $(A^{\prime }\cap B^{\prime }\cap C)\cup (B\cap C)\cup (A\cap C)$ is equal to

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

Q. Two sets given as$A=\{2,6,5,7,8,3\}$and $B=\{6,3,5,8,7,2,1\},$ then tap the bubbles having elements in $A\cap B.\$$

1. $1$
2. $2$
3. $3$
4. $4$
5. $5$
6. $6$
7. $7$
8. $8$
9. $9$
10. $0$

Q. For any two sets $A\&B,$
$A\cup B=\{x:x\in A\text{or}x\in B\}$
$A\cap B=\{x:x\in A\text{and}x\in B\}.$

1. False
2. True

Q.

If A = { $(x,y)$: $x^2+y^2=25$ } And B = {(x, y): $x^2+9y^2=144$}, then $A\cap B$ contains

1. One point

2. Three points

3. Two points

4. Four points

Q. If for a positive integer $a,aN=\{ax:x\in N\}$ and $13N\cap 7N=kN$, then the value of $k$ is

Q.

If the set of factors of a whole number $n$, including $n$ itself but not $1$ is denoted by $F\left(n\right),$ and $F\left(16\right)\cap F\left(40\right)$ = $F\left(x\right)$ then $x$ is

1. 4

2. 8

3. 6

4. 10

Q. $C$ and $D$ are two sets such that $C=\{p:p\in R,1\le p<7\}$ and set $D=\{q:q\in R-2<q\le 4\},$ then find $C\cap D.$

1. ($0,4)$
2. $(1,7)$
3. $[1,4]$
4. $(-2,4]$

Q. If the sets A and B are defined as
$A=\{x:x=2n,n\in N,n<100\}B=\{x:x=3n,n\in N,n<100\}$
then, the number of elements in $A\cap B$ is

1. 16
2. 198
3. 33
4. 59

Q. Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can formed such that $Y\subseteq X,Z\subseteq XandY\cap Z$ is empty is:

1. $5^2$
2. $3^5$
3. $2^5$
4. $5^3$

Q.

If $A$ and $B$ are two given sets, then
$A\cap (A\cap B{)}^c$ is equal to

1. $A$

2. $B$

3. $\varnothing$

4. $A\cap B^c$