Question
Download Solution PDFA relation R is said to be an equivalence relation if:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if the relation R is reflexive, symmetric, and transitive.
Ex. The relation R in the set {1, 2, 3} given by
R = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} is equivalence.
Reflexive: A relation is said to be reflexive if (a, a) ∈ R, for every a ∈ A.
Ex. The relation R in the set {1, 2, 3} given by
R = {(1,1), (2,2), (3,3)} is reflexive.
Symmetric: A relation is said to be symmetric, if (a, b) ∈ R, then (b, a) ∈ R.
Ex. The relation R in the set {a, b, c} given by
R = {(a,b), (b,a), (b,c), (c,b)} is symmetric.
Transitive: A relation is said to be transitive if (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R.
Ex. The relation R in the set {1, 2, 3} given by
R = {(1,2), (2,3), (1,3)}
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