Let R = x , y): x, y ∈ A, x + y = 5 where A = 1, 2, 3, 4, 5 then

Question

Let R = x , y): x, y ∈ A, x + y = 5 where A = 1, 2, 3, 4, 5 then (A) R is not reflexive, symmetric and not transitive (B) R is an equivalence relation (C) R is reflexive, symmetric but not transitive (D) R is not reflexive, not symmetric but transitive

Tardigrade Admin · Accepted Answer

R = (1, 4), (4, 1), (2, 3), (3, 2) ∴ R is not reflexive as (1, 1) ∉ R. Also, R is symmetric by definition and not transitive as (1, 4) ∈ R, (4, 1) ∉ R but (1, 1) ∉ R.

Q. Let $R = {{x, y) : x, y \in A, x + y = 5}$ , where $A = {1, 2, 3, 4, 5}$ , then

R is not reflexive, symmetric and not transitive

R is an equivalence relation

R is reflexive, symmetric but not transitive

R is not reflexive, not symmetric but transitive

$R = {(1, 4), (4, 1), (2, 3), (3, 2)}$ , $∴ R$ is not reflexive as $(1, 1) \in / R$ . Also, $R$ is symmetric by definition and not transitive as $(1, 4) \in R, (4, 1) \in / R$ but $(1, 1) \in / R$ .

Q. Let R={{x,y):x,y∈A,x+y=5}, where A={1,2,3,4,5}, then