Saved Bookmarks
| 1. |
Determine whether the relation R in the set A = {1,2,3,4,5,6} as R = {x,y}:y is divisible by x is reflexive, symmetric and transitive. |
|
Answer» (1) R is reflexive, as (a, a) ∈ R ⇒ a is divisible by a ∴ R is reflexive. (2) Let (1, 2) ∈ R ⇒ 2 is divisible by 1 But (2,1) ∈ R ⇒ 1 cannot divide by 2 ∴ R is not symmetric. (3) Let (1, 2)∈ R ⇒ 1(2, 4)ER ⇒ 2 is divisible by I and 4 is divisible by 2 Now, (1,4) ∈ R ⇒ 4 is divisible by 1 ∴ (1, 2)∈ R I(2,4) ∈ R ⇒ (1, 4)∈ R ∴ R is transitive. |
|