门| GATE-CS-2015(Set 1)|第44章

假设L = {p，q，r，s，t}是由以下Hasse图表示的晶格：

对于任何x，y∈L，不一定是不同的，x y和x y分别是x，y的连接和满足。令L ³ = {(x，y，z)：x，y，z∈L}是L元素的所有有序三元组的集合。令pr是元素(x，y，z)∈的概率选择的L ³等价地满足x(y)z =(x y)x(x z)。然后
(A) Pr = 0
(B) Pr = 1
(C) 0 (D) 1/5 答案： (D)
解释：

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.

这个问题的测验