Discrete Structures2080.15 marksEquivalence Relations
Let us assume that R be a relation on the set of ordered pair of positive integers such that ((a,b),(c,d))∈R((a, b), (c, d)) \in R((a,b),(c,d))∈R if and only if ad = bc. Is R an equivalence relation?
Let us assume that R be a relation on the set of ordered pair of positive integers such that ((a,b),(c,d))∈R((a, b), (c, d)) \in R((a,b),(c,d))∈R if and only if ad = bc. Is R an equivalence relation? [5]
A relation R on a set A is an equivalence relation if and only if it satisfies three properties: 1. Reflexivity: (a, a) ∈ R for all a ∈ A 2. Symmetry: If (a, b) ∈ R then (b, a) ∈ R 3. Transitivity: If (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R Here, R is defined on ordered pairs of positive intege...