Question 1189000: State the number of subsets of {p,q,r,s}. Explain the answer. Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52803) (Show Source):
You are given a set containing 4 elements (listed).
The number of all possible subsets is = 16, including the empty set and the improper subset.
The common fact is that a finite set with n elements has distinct subsets.
The solution from the other tutor shows a link to where you can see a demonstration, using combinatorics, of why a set of n elements has 2^n subsets.
A much simpler demonstration of that fact is the following:
In making a subset from a set containing n elements, you look at each element and decide whether or not to include that element in your subset. There are 2 choices to the answer to that question for each of the n elements, making the number of different subsets 2^n.
