Question

what is the power set of the set ( 1,2,3,4)

Answer 1

Answer:

In general, to find a power set, the easiest way is binary counting. What is this? The way to approach is, imagine you have n items to select. At any stage, you can choose to select an item - call it 1, or you choose not to - call it 0.

So, if you do not even want to select a single item, the choice will look:

000...000=0

n zeros.

You choose the first item, and nothing beyond:

000...001=1

n-1 zeros, followed by 1 : 1.

It is obvious that using n binary digits, we can generate 2n choices. Those choices, together, generates the power set.

In your case :

{1,{2},{3,4}}

000 → {}

001 → {1}

010 → { {2} }

011 → { 1, {2} }

…..

You got the idea.

Answer 2

Answer:

{{1,2,3,4},{1,2,3},{1,2,4},{1,3,4},{2,3,4},{1,2},{1,3},{1,4},{2,3},{2,4},{3,4},{1},{2},{3},{4}{ }}

Step-by-step explanation: