Practicing Success
A relation R in the set A = {1,2,3,4,5,6, } defined as R = {(x, y) : y is divisible by x} is- |
Reflexive and transitive only Transitive and symmetric only Reflexive and symmetric only Neither reflexive nor transitive |
Reflexive and transitive only |
A = {1,2,3,4,5,6, } R = {(x, y) : y is divisible by x} We know that any number x is divisible by itself. ⇒ (x, x) ∈ R So, R is reflexive, But, (4, 2) ∉R [as 4 is divisible by 2] So, R is not symmetric. Let (x, y), (y, z) ∈ R , then Y is divisible by x and x is divisible by y. So, z is divisible by x. ⇒ (x, z) ∈ R So, R is transitive. Hence, r is reflexive and transitive but not symmetric. |