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GradeIntersection of Sets

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If A and B are two sets, $n\left( A-B \right)=8+2x$, $n\left( B-A \right)=6x$ and $n\left( A\cap B \right)=x$. If $n\left( A \right)=n\left( B \right)$, then $n\left( A\cap B \right)$

(a). 26

(b). 50

(c). 24

(d). None of these

(a). 26

(b). 50

(c). 24

(d). None of these

Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number) . Then $n\left( X\cap Y \right)=$ :

1) 4

2) 6

3) 8

4) 12

1) 4

2) 6

3) 8

4) 12

If ${N_a}$ is equal to $\{ an:n \in N\} $, then find ${N_5} \cap {N_7}$

1). ${N_7}$

2). $N$

3). ${N_{35}}$

4). ${N_5}$

1). ${N_7}$

2). $N$

3). ${N_{35}}$

4). ${N_5}$

If we are given the sets $A=\left\{ 3,5,7,9,11 \right\},B=\left\{ 7,9,11,13 \right\},C=\left\{ 11,13,15 \right\}$ and $D=\left\{ 15,17 \right\}$, find $A\cap C$.

If we are given the sets as $A=\left\{ 2x:x\in N \right\}$, $B=\left\{ 3x:x\in N \right\}$ and $C=\left\{ 5x:x\in N \right\}$ then $\left( A\cap B\cap C \right)$ is equal to?

(a) {15, 30, 46, ……}

(b) {10, 20, 30, ……}

(c) {30, 60, 90, ……}

(d) {7, 14, 21, ……}

(a) {15, 30, 46, ……}

(b) {10, 20, 30, ……}

(c) {30, 60, 90, ……}

(d) {7, 14, 21, ……}

In a class, 60% of the students pass in Hindi, and 45% pass in Sanskrit. If 25% of them pass in both subjects, what percentage of the students fails in both subjects?

(a) 80%

(b) 20%

(c) 25%

(d) 75%

(a) 80%

(b) 20%

(c) 25%

(d) 75%

Let A and B be the two sets such that \[n\left( A-B \right)=60+3x\], \[n\left( B-A \right)=8x\] and \[n\left( A\cap B \right)=x-4\] then draw a Venn diagram to illustrate this information. If \[n\left( A \right)=n\left( B \right)\] then find

(a) The value of \[x\]

(b) \[n\left( A\cup B \right)\]

(a) The value of \[x\]

(b) \[n\left( A\cup B \right)\]

If $X = \{ a,b,c,d\} $and $Y = \left\{ {f,b,d,g} \right\}$ find

i.$X - Y$

ii.$Y - X$

iii.$X \cap Y$

i.$X - Y$

ii.$Y - X$

iii.$X \cap Y$

In a group of 500 people, 310 can speak Hindi, 260 can speak English. How many people can speak both English and Hindi?

Find sets A,B and C such that $A\cap B$, $B\cap C$ and $A\cap C$ are non-empty sets and $A\cap B\cap C=\varnothing $.

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

(i)A\[ \cap \]B

(ii)A \[ \cap \]C

(iii)A \[ \cap \]D

(iv)B \[ \cap \]C

(v)B \[ \cap \]D

(vi)C \[ \cap \]D

(i)A\[ \cap \]B

(ii)A \[ \cap \]C

(iii)A \[ \cap \]D

(iv)B \[ \cap \]C

(v)B \[ \cap \]D

(vi)C \[ \cap \]D

Complete the following statement

1. $A\cap B=B\Rightarrow B.......A$

1. $A\cap B=B\Rightarrow B.......A$

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