Definition of a Set

Q. If $A$ and $B$ are two mutually exclusive events, then the relation between $P\left(\overline{A}\right)$ and $P\left(B\right)$ is

1. $P\left(B\right)\ge P\left(\overline{A}\right)$
2. $P\left(B\right)\le P\left(\overline{A}\right)$
3. $P\left(B\right)=P\left(\overline{A}\right)$
4. $P\left(B\right)<P\left(\overline{A}\right)$

Q. Let set A = {6, 8, 10, 12} and set B = {3, 9, 15, 18}.

Insert the symbol '$ϵ$' or '$\text{/}ϵ$' to make true: 18…….B

Q. Is the following collection, a set? Justify your answer:

(iv) The collection of most talented writers of India

Q. Assertion(A) : A random variable $X$ takes the values $0,1,2.$ It's mean is $\mathrm{0.6.}$ If $P(X=0)=0.5,$ then $P(X=1)=0.4$

Reason(R) : $X:S\to R$ is a descreate random variable with range $\{X_1,X_2,X_3,\cdots \}$ then mean $=\sum _{r=1}^{\infty }{x}_{r}P(X=x_r)$

1. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
2. Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
3. $A$ is true but $R$ is false
4. $A$ is false but $R$ is true

Q. Let $U$ be the set of all triangles in a plane. If $A$ is the set of all triangles with at least one angle different from ${60}^{\circ },$ what is $A^{\prime }?$

Q. Write the following sets in set builder (Rule Method) form:
$B_5=\text{{-5, -4, -3, -2, -1}}$

Q. If X is a set of odd natural numbers greater than 12, then tap the bubbles that are true for the set X.

1. $13\in X$
2. $8\in X$
3. $15\notin X$
4. $4\notin X$
5. $25\notin X$
6. $24\notin X$
7. $37\in X$
8. $49\in X$
9. $52\in X$
10. $54\notin X$

Q. A collection of all multiples of 3 less than 91 is

1. a set.
2. not a set.