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Given the 7-element set A = { a,b,c,d,e,f,g }. Find a collection T of 3-element subsets of A such that each pair of elements from A occurs exactly in one of the subsets of T.
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We can make $T$ by taking two disjoint $3$ elements subsets of A.
Eg. T={{$a,b,c$},{$d,e,f$}} but we cannot include all the elements.