Complement of a Set

Q. If $n\left(A\right)=52$, $n(A\cup B)=80$, $n(A\cap B)=31,$ then $n(A\cap B^{\prime })=$

1. $11$
2. $21$
3. $31$
4. $42$

Q. In a town of $10000$ families, it was found that $40\%$ families buy newspaper $A$, $20\%$ buy newspaper $B$ and $10\%$ buy newspaper $C$, $5\%$ families buy $A$ and $B$, $3\%$ buy $B$ and $C$ and $4\%$ buy $A$ and $C$. If $2\%$ families buy all the three newspapers, then number of families which buy newspaper $A$ only is

Q.

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 2, 3, 4}

Then, $A^c$ is

1. {1, 2, 3, 4}

2. {5, 6, 7, 8, 9, 10}

3. {2, 3, 4, 5, }

4. None of these

Q. If $n\left(U\right)=48,n\left(A\right)=28,n\left(B\right)=33$ and $n(B–A)=12$, then $n(A\cap B{)}^C=$

Q. If $U$ is the Universal set and $A$ is a subset of $U$, then $A^{\prime }=U-A$.

1. False
2. True

Q. If $U=\{1,3,5,7,9\}$ and $A=\{3,5,7\}$, then $(A^{\prime }{)}^{\prime }$ is:

1. $\{3,5,7\}$
2. $\{1,9\}$
3. $\{1,3,9\}$
4. $\{1,3,5,7,9\}$

Q. Match the following shaded portions of venn diagram representation of two sets $A,B$.

1. $(B\cup A^{\prime })$
2. $(A\cap B{)}^{\prime }$
3. $(A\cup B{)}^{\prime }$

Q. A group of $123$ workers went to a canteen for cold drinks, ice-cream and tea. $42$ workers took ice-cream, $36$ took tea and $30$ took cold drinks. $15$ workers purchased ice-cream and tea, $10$ purchased ice-cream and cold drinks, and $4$ purchased cold drinks and tea but not ice-cream. Then the number of workers who did not purchase anything is

Q. Let $U=\{1,2,3,4,5,6,7,8,9,10\}$. If $A=\{1,2,5\}$ and $B=\{6,7\},$ then $A\cap B^{\prime }$ is

1. $B$
2. $A$
3. $A^{\prime }$
4. $B^{\prime }$

Q. For a given set $A$ as shown in the diagram below, $A^{\prime }=$

1. $\{5,10,20\}$
2. $\{12,14,16,18\}$
3. $\{5,10\}$

Q.

For all sets $A$ and $B$, $A-(A\cap B)$ is equal to

1. $A^{\prime }\cap B$

2. $A\cap B^{\prime }$

3. $A^{\prime }\cap B^{\prime }$

4. $(A\cup B{)}^{\prime }$

Q. If $U$ is the Universal set and $A$ is a subset of $U$, then $A^{\prime }=U-A$.

1. False
2. True

Q. If $U=\text{set of the first 6 prime numbers}$ and $A=\text{set of even prime numbers}$, then $A^{\prime }=$

1. $\{3,5,7,11,13\}$
2. $\left\{2\right\}$
3. $\{2,3,5,7\}$

Q.

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 2, 3, 4}

Then, $A^c$ is

1. {1, 2, 3, 4}

2. {5, 6, 7, 8, 9, 10}

3. {2, 3, 4, 5, }

4. None of these

Q.

If U = {2, 4, 6, 8, 10, 12, 14} and
A = {2, 4, 10}, where U is the Universal set .
Which of the following is A^C?

1. {2, 4, 6, 8}

2. {6, 8, 12, 14}

3. {4, 10, 12, 14}

4. {8, 6, 10}