Counting Disjoint Pairs

Problem

Let $M$ be a set with $6$ elements, and define

T = \left\{(A, B) \mid A, B \subseteq M,\ A \neq \varnothing,\ B \neq \varnothing,\ A \cap B = \varnothing\right\}.

Find the number of elements of $T$ .

Answer

Solution

Difficulty	5/10
Topics	combinatorics, Counting, Set Theory

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