Question 1106507: If A={5,3,3,7} List all the subsets of A set.
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
This post has a pitfall: the list of elements contains two identical names.
There is nothing criminal or fatal in it: you can meet such cases in Math or even in real life.
For example, if a polynomial has multiple roots, then the list of the roots may contain identical numbers.
Or a human family may have TWINS. // But even then the parents give different names to the children . . . (as a rule).
Or a list of voters can contain identical names, when they relate to different people.
As well as the list of people/abonents in a telephone book . . .
But, in such cases, if the author of a mathematical text (including the person who originated this post/(posted text))
wants to be mathematically correct, he (or she) must explain WHY he (or she) did include two (or more) identical names
in the element list of the set. A good style and a common sense requires it . . .
If such an explanation is absent, then BY DEFAULT the identical names are considered as describing
the presence of different elements (different "copies") in the set.
After this PREFACE, read my response to your problem.
List AS MANY subsets as you can ON YOUR OWN.
Then post your results to the forum.
We will check it.
Together with the empty subset and with the improper subset (which coinsides with the given set) the total number of subsets
in this case is  = 16.
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See the lesson
- How many subsets are there in a given finite set of n elements?
in this site.
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