Suppose ℒ = {𝑝, 𝑞, 𝑟, 𝑠, 𝑡} is a lattice represented by the following Hasse diagram: For any x, y ϵ ℒ not necessarily distinct x ⋁ y and x ⋀ y are join and meet of x, y respectively. Let ℒ 3 = {(x, y, z): x, y, z ϵ ℒ } be the set of all ordered triplets of the elements of ℒ. Let p r be the probability that an element (x, y, z) ϵ ℒ 3 chosen equiprobably satisfies x ⋁ (y ⋀ z) = (x ⋁ y) ⋀ (x ⋁ z). Then

GATE Computer Science (CS) 2015 Shift 1 Solved Paper

Question : 42 of 65

Marks: +1, -0

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

For any x, y ϵ ℒ not necessarily distinct x ⋁ y and x ⋀ y are join and meet of x, y respectively. Let ℒ³= {(x, y, z): x, y, z ϵ ℒ } be the set of all ordered triplets of the elements of ℒ. Let p_r be the probability that an element (x, y, z) ϵ ℒ³chosen equiprobably satisfies x ⋁ (y ⋀ z) = (x ⋁ y) ⋀ (x ⋁ z). Then

p_r = 0
p_r = 1
$0 < p_{r} ≤ \;{1}/{5}$
$\;{1}/{5} < p_{r} < 1$

Validate

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