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Lilia
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Mod note: Moved from a technical math forum, so missing the homework template.
Given a set A = {a1, a2, ..., an} and its two subsets - X, Y so that these subsets satisfy a condition, find the number of such possible (X, Y) pairs
Condition 1: X ∩ Y = {a1, a2},
Condition 2: X ⊆ Y,
Condition 3: | (X - Y) ∪ (Y - X) | = 1
I've tried to solve these but I still can't figure out the right way to think when solving these.
For X ∩ Y = ∅ the number of subsets is ΣC(n,k) × 2n-k, where k=0÷n.
This is how I think - so, for Condition 1, X and Y should have only a1 and a2 in common and can have other distinct elements, so we need to choose those two elements but how to choose them for both X and Y?
For Condition 2, |X| can be k, |Y| can be k (or k-1?), therefore the number of subsets - C(n,k) × C(n,k) = (C(n,k))2? Is this right?
For Condition 3, X is a subset of Y, or Y is a subset of X, and they have one element in common, right? If so, how to count the number of subsets?
Given a set A = {a1, a2, ..., an} and its two subsets - X, Y so that these subsets satisfy a condition, find the number of such possible (X, Y) pairs
Condition 1: X ∩ Y = {a1, a2},
Condition 2: X ⊆ Y,
Condition 3: | (X - Y) ∪ (Y - X) | = 1
I've tried to solve these but I still can't figure out the right way to think when solving these.
For X ∩ Y = ∅ the number of subsets is ΣC(n,k) × 2n-k, where k=0÷n.
This is how I think - so, for Condition 1, X and Y should have only a1 and a2 in common and can have other distinct elements, so we need to choose those two elements but how to choose them for both X and Y?
For Condition 2, |X| can be k, |Y| can be k (or k-1?), therefore the number of subsets - C(n,k) × C(n,k) = (C(n,k))2? Is this right?
For Condition 3, X is a subset of Y, or Y is a subset of X, and they have one element in common, right? If so, how to count the number of subsets?
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