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

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

Topic-wise GATE CS PYQs with verified steps