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Number of Elements in a Cartesian Product

Prove that if...

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Prove that if A has n element then it's power set has 2'n element!

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Q. If a set has

n

elements, then it has subsets.

A

B

are two finite sets, such that

A

p

B

q

elements. The number of elements in the power set of

A

48

more than number of elements in the power set of

B .

Then select the correct statement about

p & q .

S

is any set, then the family of all the subsets of

S

is called the power set of

S

and it is denoted by

P (S)

. Power set of a given set is always non-empty. If

A

has n elements, then

P (A)

S

T

are two sets such that

S

21

elements. T has

32

S

\cap

T

11

elements, then find the number of elements in

S

\cup

T

If S and T are two sets such that S has 21 elements T has 32 elements and $S \cap T$ has 11 elements, how many elements does $S \cup T$ have?

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