Complement of a Set

Q. For any set $A,$ if $U$ is the universal set, then $A^{\prime }=$

1. $\{x:x\notin A\mathrm{and}x\in U\}$
2. $\{x:x\in A\}$
3. $\{x:x\in U\}$

Q. If $A$ and $B$ are two sets such that $(A-B)\cup B=A$, then

1. $B\subseteq A$
2. $A\subseteq B$
3. $A=B$
4. $A\cap B=A$

Q. Two newspapers $A$ and $B$ are published in a city. It is known that $30\%$ of the city population read $A$ and $25\%$ read $B$, while $10\%$ read both $A$ and $B$. Further, $20\%$ of those who read $A$ but not $B$ look into sports news and $40\%$ of those who read $B$ but not $A$ also look into sports news, while $50\%$ of those who read both $A$ and $B$ look into sports news. Then the percentage of the population who look into sport news, is

1. $15$
2. $13$
3. $17.5$
4. $12.7$

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

1. $27$
2. $28$
3. $29$
4. $30$

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}

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

1. False
2. True

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.

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 $n(A\cap B{)}^C=$

1. $27$
2. $28$
3. $29$
4. $30$

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 $U=\{a,b,c,d,e,f,g,h\},$
$P=\{a,b,c,f\},Q=\{d,g,f,h\},$
$\text{then which of the following are correct?}$

1. $(P\cup Q{)}^{\prime }=\{e\}$
2. $(P-Q{)}^{\prime }=\{d,e,f,g,h\}$
3. $(P\cup Q{)}^{\prime }=P^{\prime }\cap Q^{\prime }$
4. $P\cap {\varphi }^{\prime }=\{a,b,c,f\}$

Q. If $A$ and $B$ are two sets such that $(A-B)\cup B=A$, then

1. $B\subseteq A$
2. $A\subseteq B$
3. $A=B$
4. $A\cap B=A$

Q. For three sets $A,B$ and $C,A\cap (B-C)=$

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

Q. For three sets $A,B$ and $C,A\cap (B-C)=$

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

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 $U=\text{set of the first 6 prime numbers}$ 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. For three sets $A,B$ and $C,A\cap (B-C)=$

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

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 $U=\text{set of the first 6 prime numbers}$ 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. 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. If $U=\{a,b,c,d,e,f,g,h\},$
$P=\{a,b,c,f\},Q=\{d,g,f,h\},$
$\text{then which of the following are correct?}$

1. $(P\cup Q{)}^{\prime }=\{e\}$
2. $(P-Q{)}^{\prime }=\{d,e,f,g,h\}$
3. $(P\cup Q{)}^{\prime }=P^{\prime }\cap Q^{\prime }$
4. $P\cap {\varphi }^{\prime }=\{a,b,c,f\}$