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Suppose L = {p, q, r, s, t} is a lattice represented by the following Hasse diagram:
 
For any x, y ∈ 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 ∈ L} be the set of all ordered triplets of the elements of L. Let pr be the probability that an element (x,y,z) ∈ L3 chosen equiprobably satisfies x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z). Then
  • a)
    Pr = 0
  • b)
    Pr = 1
  • c)
    0 < Pr ≤ 1/5
  • d)
    1/5 < Pr < 1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Suppose L = {p, q, r, s, t} is a lattice represented by the following ...
Number of triplets in L3 = Number of ways in which we can choose 3 elements from 5 with repetition = 5 * 5 * 5 = 125.
Now, when we take x = t, then the given condition for L is satisfied for any y and z. Here, y and z can be taken in 5 * 5 = 25 ways.
Take x = r, y = p, z = p. Here also, the given condition is satisfied. So, pr > 25 / 125 > 1/5.
For x = q, y = r, z = s, the given condition is not satisfied as q ⋁ (r ⋀ s) = q ⋁ p = q, while (q ⋁ r) ⋀ (q ⋁ s) = t ⋀ t = t.
So, pr ≠ 1.
Hence D choice.
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Suppose L = {p, q, r, s, t} is a lattice represented by the following Hasse diagram:For any x, y ∈ 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 ∈ L} be the set of all ordered triplets of the elements of L. Let pr be the probability that an element (x,y,z) ∈ L3chosen equiprobably satisfies x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z). Thena)Pr = 0b)Pr = 1c)0 < Pr ≤ 1/5d)1/5 < Pr < 1Correct answer is option 'D'. Can you explain this answer?
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Suppose L = {p, q, r, s, t} is a lattice represented by the following Hasse diagram:For any x, y ∈ 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 ∈ L} be the set of all ordered triplets of the elements of L. Let pr be the probability that an element (x,y,z) ∈ L3chosen equiprobably satisfies x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z). Thena)Pr = 0b)Pr = 1c)0 < Pr ≤ 1/5d)1/5 < Pr < 1Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Suppose L = {p, q, r, s, t} is a lattice represented by the following Hasse diagram:For any x, y ∈ 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 ∈ L} be the set of all ordered triplets of the elements of L. Let pr be the probability that an element (x,y,z) ∈ L3chosen equiprobably satisfies x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z). Thena)Pr = 0b)Pr = 1c)0 < Pr ≤ 1/5d)1/5 < Pr < 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose L = {p, q, r, s, t} is a lattice represented by the following Hasse diagram:For any x, y ∈ 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 ∈ L} be the set of all ordered triplets of the elements of L. Let pr be the probability that an element (x,y,z) ∈ L3chosen equiprobably satisfies x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z). Thena)Pr = 0b)Pr = 1c)0 < Pr ≤ 1/5d)1/5 < Pr < 1Correct answer is option 'D'. Can you explain this answer?.
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