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GATE CS 2015 Set 1 — Question 42

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MCQ+2 / -0.67HardPartial Orders & LatticesSets & CombinatoricsEngineering MathematicsSample Space & EventsProbability & Statistics

Engineering Mathematics → Probability & Statistics → Partial Orders & Lattices

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Question

Suppose L={p,q,r,s,t}L = \{p, q, r, s, t\} is a lattice represented by the following Hasse diagram:
Hasse diagram of a lattice L

For any x,y∈Lx, y \in L, not necessarily distinct, x∨yx \lor y and x∧yx \land y are join and meet of x,yx, y, respectively. Let L3={(x,y,z):x,y,z∈L}L^3 = \{(x, y, z): x, y, z \in L\} be the set of all ordered triplets of the elements of LL. Let prp_r be the probability that an element (x,y,z)∈L3(x, y, z) \in L^3 chosen equiprobably satisfies x∨(y∧z)=(x∨y)∧(x∨z)x \lor (y \land z) = (x \lor y) \land (x \lor z). Then
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