Power Set

Power set of the set is defined as the family consisting of all subset of a set.

It is denoted by  P.

\{A | A \subset B\} is power set of  B .

It can be written as

P=\{A | A \subset B\}

Example:

A = \{1,2\}

P {A} =\{\{\}, \{1\},\{2\},\{1,2\}\}

 \rightarrow Number of element in a finite set A is denoted by n (A) .

 \rightarrow Number of elements in Power set of a set  A having  m elements is  2^m.

Example:

 n(A) =4 , n (P(A)) =2^4 =16

\rightarrow \phi \times A = \phi .

\rightarrow  R \times R =\{(x,y) ; x \in R , y \in R\}

\rightarrow  N \times N =\{(x.y) : x \in N, y \in N\}

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