Question

if A={l,m,n} then write the power set of A​

Answer 1

Easy! If the original set has n members, then the Power Set will have 2n members

Example: {a,b,c} has three members (a,b and c).

So, the Power Set should have 23 = 8, which it does, as we worked out before.

Notation

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

|P(S)| = 2n

Example: for the set S={1,2,3,4,5} how many members will the power set have?

Well, S has 5 members, so:

|P(S)| = 2n = 25 = 32

You will see in a minute why the number of members is a power of 2

It's Binary!

And here is the most amazing thing. To create the Power Set, write down the sequence of binary numbers (using n digits), and then let "1" mean "put the matching member into this subset".

So "101" is replaced by 1 a, 0 b and 1 c to get us {a,c}

Like this:

abc Subset

0 000 { }

1 001 {c}

2 010 {b}

3 011 {b,c}

4 100 {a}

5 101 {a,c}

6 110 {a,b}

7 111 {a,b,c}

Well, they are not in a pretty order, but they are all there.