Let A be a set and suppose x A Describe PA U x SolutionGiven

Let A be a set, and suppose x A. Describe P(A U {x}).

Solution

Given: A be a set

           and x is not in A

then power set P(A u {x}).

              if set A contain {a,b}

S=(A u {x})= {a,b,c,x} we get the Power Set of {a,b,x}:

P(S) = { {}, {a}, {b}, {x}, {a, b}, {a, x}, {b, x}, {a, b, x} }

   

The number of members of a set is often written as |S|, so we can write:

                                                    |P(S)| = 2ⁿ

Here we have 3 lement in S and have 2^3=8 sub sets