Subsets

I have two subset equations here, could someone give me a rough idea how to do either?

Let A = {1,2,3,4}. List all the subsets B of A such that

1) B is not a subset of {1,2}
2) {1,2} is a proper subset of B

Any help for either would be greatly appreciated. Thanks

Quote:

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Originally Posted by GreenDay14

I have two subset equations here, could someone give me a rough idea how to do either?

Let A = {1,2,3,4}. List all the subsets B of A such that

1) B is not a subset of {1,2}
2) {1,2} is a proper subset of B

Any help for either would be greatly appreciated. Thanks

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For 1) you have to find all subsets of A that don't contain 1 and 2 simultaneously : Subsets of 1 element you have all 4, of two elements you could have 6, but of those one is {1,2} so you can only have 5, of three elements you could have 4 but two are {1,2,3} and {1,2,4} so you can only have 2, and finally you can't have the whole set since it contains 1 and 2. So now just list these subsets: there are 12 (including the empty set)

For 2) the reasoning is analogous, only now you have to find the subsets that have 1 and 2

Quote:

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Originally Posted by Jose27

For 1) you have to find all subsets of A that don't contain 1 and 2 simultaneously : Subsets of 1 element you have all 4, of two elements you could have 6, but of those one is {1,2} so you can only have 5, of three elements you could have 4 but two are {1,2,3} and {1,2,4} so you can only have 2, and finally you can't have the whole set since it contains 1 and 2. So now just list these subsets: there are 12 (including the empty set)

For 2) the reasoning is analogous, only now you have to find the subsets that have 1 and 2

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I don't understand what you are saying for the first one? Are you saying that there is zero, since all of the elements have a 1 or 2 in them?

and in the second one are you saying that the answer is say: {1,2}, {1,2,3}, {1,2,4}, ?