MathDB

Let

S

be a finite set of size

s\geq 1

defined with a uniform probability

\mathbb{P}

( i.e. for any subset

X\subset S

of size

x

\mathbb{P}(x)=\frac{x}{s}

). Suppose

A

and

B

are subsets of

S

. They are said to be independent iff

\mathbb{P}(A)\mathbb{P}(B)=\mathbb{P}(A\cap B)

. Which if these is sufficient for independence?
(A)

|A\cup B|=|A|+|B|

(B)

|A\cap B|=|A|+|B|

(C)

|A\cup B|=|A|\cdot |B|

(D)

|A\cap B|=|A|\cdot |B|

Problem Statement