Complement of a Set

Q.

If U = {a, b, c, d, e, f, g, h}, find the complement of the following sets :

(i) A = {a, b, c} (ii) B = {d, e, f, g}

(iii) C = {a, c, e, g} (iv) D = {f, g, h, a}

Q. Show that $A\cap B=A\cap C$ need not imply $B=C$

Q.

If E and F are events such that $P\left(E\right)=\frac{1}{4},$
$P\left(F\right)=\frac{1}{2}$ and$P\left(\text{E and F}\right)$ $=\frac{1}{8}$ Find
$\text{(i) P (E or F) (ii) P (not E and not F)}$

Q. 32. if Z1, Z2 are two nonzero complex number such that |Z1+Z2|=|Z1| +|Z2| then amp (Z1/Z2) is equal too

Q. For any set $A,A\cap A^{\prime }\ne \varnothing .$

1. False
2. True

Q. 11. Two finite sets A and B have P and Q elements respectively such that P is greater than Q the number of subsets of the power set of A 240 more than the total number of subsets of power Set B then what is the value of P + q

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. For any two sets $A\&B,A\cup B$ is represented as:

1. 
2. 
3.