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Set Theoryhard
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Let S={2,3,4,5,6,7,8,9,10}S = \{2, 3, 4, 5, 6, 7, 8, 9, 10\}S={2,3,4,5,6,7,8,9,10}. A subset A⊆SA \subseteq SA⊆S is called "pairwise coprime" if any two distinct elements in AAA have a greatest common divisor of 1. What is the maximum possible cardinality of such a subset AAA?