1) Reflexive only 2) Transitive only 3) Symmetric only 4) An equivalence relation Solution: (4) If R is a relation, xRy ⇔ x − y is divisible... View Article
1) Reflexive only 2) Symmetric but not transitive 3) Equivalence 4) None of the above Solution: (3) Consider A = {a, b, c} R: {(a, a}, (b,... View Article
1) aR1 b ⇔ |a| = |b| 2) aR2b ⇔ a ≥ b 3) aR3 ⇔ a divides b 4) aR4 ⇔ a < b Solution: (1) (i) |a| = | b| Reflexive: (a, a) ∈ R a = a... View Article
1) Reflexive, transitive but not symmetric 2) Reflexive, transitive but not symmetric 3) Symmetric, Transitive but not reflexive 4) Neither... View Article
1) Reflexive 2) Symmetric and transitive 3) Reflexive and symmetric 4) Reflexive and transitive Solution: (2) A = {0} Set A is not reflexive.... View Article
1) Reflexive 2) Symmetric 3) Transitive 4) None of these Solution: (3) aRa ⇒ R is not reflexive (a, b) ∈ R (b, a) does not belong to R R is... View Article
1) Every (a, b) ϵ R 2) No (a, b) ϵ R 3) No (a, b), a ≠b, ϵ R 4) None of these Solution: (3) A relation R on a set A such that for all a, b ∈... View Article
1) Symmetric 2) Antisymmetric 3) Equivalency relation 4) None of these Solution: (2) a] A ⊂ A (A, A) ∈ R is reflexive b] (a, b) ∈ R (b, a)... View Article
1) Reflexive 2) Symmetric 3) Transitive 4) None of these Solution: (2) Let (a, b) ∈ R Then (a, b) ∈ R ⇒ (b, a) ∈ R-1 (b, a) ∈ R [Because R... View Article
1) Reflexive but not symmetric 2) Symmetric but not transitive 3) Symmetric and transitive 4) None of the above Solution: (1) aRb ⇔ b is... View Article
1) Reflexive and symmetric but not transitive 2) Reflexive and transitive but not symmetric 3) Symmetric, transitive but not reflexive 4)... View Article