Is relation defined over the set of integers as follows
R is a relation defined over the set of integers Z as follows "aRb iff a is a factor of b". Then R is
- A.
Reflexive, Symmetric but not Transitive
- B.
Symmetric, Transitive but not Reflexive
- C.
Reflexive, Transitive but not Symmetric
- D.
Reflexive, Symmetric and Transitive
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Correct answer: C
Given : (a,b) ∈ R ⇒ a is a factor of b
(a,a) ∈ R, since a is a factor of a; ∴ R is reflexive
(a,b) ∈ R but (b,a) ∉ R, since if a is a factor of b, b is a multiple of a but not factor. ∴ R is not symmetric
But (a,b) ∈ R and (b,c) ∈ R, then (a,c) ∈ R ∴ R is transitive