Complement of a Set

Q.

If A, B and C are three events such that P(B) =$\frac{3}{4},P(A\cap B\cap C^{\prime })=\frac{1}{3}andP(A^{\prime }\cap B\cap C^{\prime })=\frac{1}{3},$ then $P(B\cap C)$ is equal to

1. $\frac{1}{12}$

2. $\frac{1}{6}$

3. $\frac{1}{15}$

4. $\frac{1}{9}$

Q. If $A,B,C$ are mutually independent events, such that $0<P\left(A\right),P\left(B\right),P\left(C\right)<1,$ then which of the following statement(s) is/are correct ?
$I.A$ and $B\cup C$ are independent events.
$II.A$ and $B\cap C$ are independent events.

1. Only $II$ is true
2. Both are true
3. Both are false
4. Only $I$ is true

Q.

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

A = {1, 2, 3, 4}

The set A^I is

1. {5, 6, 7, 8, 9, 10}

2. {1, 2, 3, 4}

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

4. None of these

Q.

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

1. ∅

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

3. B

4. A

Q.

${\left[\right(B^{\prime }\cup (B^{\prime }-A)\left)\right]}^{\prime }$ =___

1. A

2. B

3. A - B

4. B - A

Q.

If $n\left(U\right)=700,n\left(A\right)=200,n\left(B\right)=300$ and $n(A\cap B)=100,$ then $n(A^{\prime }\cap B^{\prime })=$ ___.

1. 400

2. 300

3. 200

4. 600

Q.

If ∪ = {2, 4, 6, 8, 10, 12, 14, 17}, where ∪ is Universal set and some set A = {1, 4, 6, 9, 11, 12}, then set A^C is ________.

1. can't be determined

2. {4, 6, 8, 10, 14, 17}

3. {2, 8, 10, 14, 17}

4. {1, 2, 8, 10, 14, 17}

Q. $\text{If}n(\cup )=700,n\left(A\right)=200,n\left(B\right)=300$ and $n(A\cap B)=100,$ then $n(A^{{}^{\prime }}\cap B^{{}^{\prime }})=$ ___.

1. 240

2. 300

3. 500

4. 400

Q.

If A and B are two disjoint sets, then A - B = ______.

Q.

${\left[\right(A^{\prime }\cup B^{\prime })-A]}^{\prime }$=___

1. A

2. B

3. B - A

4. A - B