Question

write all subsets of a set {2,3,4}
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Answer 1

Answer:

In general, a set with N elements has 2N subsets. This works when you get to infinite sets and their cardinal numbers too. 23=8 subsets

Step-by-step explanation:

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Answer 2

Answer:

The subsets of {1, 2, 3, 4}, by which presumably is meant the proper subsets. Thus the empty set and the universal set would not be included. The subsets can be found by taking the members of the universal set one at a time, then taking the selections from the universal set two at a time and the selections from the universal set three at time. The number of selections aka combinations is given by n!/[r!.[n - r]!] where r objects are being selected from n objects. The factorial function is defined as: n.[n - 1]. … 2.1 For example if n = 4 and r = 2, the number of selections is equal to the number of subsets in that case, which is [4.3.2.1]/[[2.1].[2.1]]. which is six.

With the above information it should be straight forward to find the number of selections for n = 4 and r = 3 and add the numbers of combinations together and that gives the number of [proper] subsets. That is adding the number of combinations for n = 4 and r = 1, 2, 3 in turn and then adding the numbers of selections to give the number of subsets.