SOLUTION: Let A equals={14,15,16,17,18,20}. a. How many subsets does A​ have? b. How many proper subsets does A​ have?

Algebra ->  Subset -> SOLUTION: Let A equals={14,15,16,17,18,20}. a. How many subsets does A​ have? b. How many proper subsets does A​ have?      Log On


   

Question 1062089: Let A equals={14,15,16,17,18,20}.
a. How many subsets does A​ have?
b. How many proper subsets does A​ have?
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
There are 6 elements in A.
a. Therefore there are +2%5E6+=+64+ subsets of A.
b. There are 63 proper subsets of A (the a. answer includes all elements of A as a subset of A, which is not a proper subset).

The number of subsets of a set of k elements is 2%5Ek because each element can either be IN a subset or NOT IN a subset. So for each element you have a binary choice whether to include it or not. This choice applies to each of k elements, giving rise to +2%5Ek+ possibilities.
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Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
On this subject, see also the lesson
    - How many subsets are there in a given finite set of n elements?
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Miscellaneous word problems".