Consider the set S = {a,b,c,d}. Consider the following 4 partitions π₁, π₂,…
GATE · 2007 · CS
Consider the set S = {a,b,c,d}. Consider the following 4 partitions π₁, π₂, π₃, π₄ on S: π₁ = {{a,b,c,d}}, π₂ = {{a,b},{c,d}}, π₃ = {{a,b,c},{d}}, π₄ = {{a},{b},{c},{d}}. Let ≺ be the partial order on the set of partitions S′ = {π₁,π₂,π₃,π₄} defined as follows: πᵢ ≺ πⱼ if and only if πᵢ refines πⱼ. The poset diagram for (S′,≺) is:
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