power set

The cardinally of the power set of $$\left\{ {0,1,2,\,\,....,\,\,10} \right.\left. \, \right\}$$ is _____________.

For a set A, the power set of A is denoted by 2 A . If A = {5, {6}, {7}}, which of the following options are TRUE? I. $$\phi \in {2^A}$$ II. $$\phi \subseteq {2^A}$$ III. $$\left\{...

Let $$\sum \, $$ be a finite non - empty alphabet and let $${2^{\sum {{}^ * } }}$$ be the power set of $$\sum {{}^ * .\,} $$ Which one of the following is TRUE ?

(a) $$S = \left\{ { < 1,2 > ,\, < 2,1 > } \right\}$$ is binary relation on set $$A = \left\{ {1,2,3} \right\}$$. Is it irreflexive? Add the minimumnumber of ordered pairs to $$S$$...

Let P(S) denote the power set of a set S. Which of the following is always true?

The number of elements in the power set $$P(S)$$ of the set $$S = \left\{ {\left\{ \phi \right\},1,\left\{ {2,3} \right\}} \right\}$$ is

Let $${\rm A}$$ be a finite set of size $$n$$. The number of elements in the power set of $${\rm A} \times {\rm A}$$ is