Question

If A and B are 2 sets such that A is a subset of B
A={1,2,3,4,5} B={4,5,6,7,8} C={7,8,9,10,11} D={10,11,12,13,14}

Find....(in picture)

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Answer 1

Answer:

The question is really "how many subsets of {1,3,5,7,11,17} are there, not counting the null set?"

As you said each element is either in the subset or it isn't. Thus each element has two choices, so there are 2⋅2⋅2⋅2⋅2⋅2=26 subsets, and we subtract one more since we also just counted the null set, which we don't want.

This may be easier to see with two elements, {a,b}. If 1 represents "in the subset" and 0 represents "not in the subset" then all possible subsets are

0,0, or ∅

0,1, or {b}

1,0, or {a}

1,1, or {a,b}