Question

Let R = {(x, y): x, y belong to 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​

Answer 1

Let R = {(x, y): x, y belong to A, X + y = 5) where A = {1, 2, 3, 4, 5) then

=> ) R is not reflexive, not symmetric but transitive.

Answer 2

Answer:

(A) R is not reflexive, symmetric and not transitive.

Step-by-step explanation:

Given, R = {(x, y) : x, y € A , x + y = 5 }

When x = 1,

1 + y = 5

=> y = 4

When x = 2,

2 + y = 5

=> y = 3

When x = 3,

3 + y = 5

=> y = 2

When x = 4,

4 + y = 5

=> y = 1

Therefore, R = { (1,4),(2,3),(3,2),(4,1) }

Reflexive:

The given relation is not reflexive. Since (1,1),(2,2),(3,3),(4,4) and (5,5) not belong to R.

Symmetric:

The given relation is symmetric. Since (1,4) belongs to R and (4,1) also belongs to R . Similarly, (2,3) belongs to R and (3,2) also belongs to R .

Transitive:

The given relation is not transitive .Since, (1,4),(4,1) belongs to R but (1,1) doesn't belong to R.

Equivalence:

The given relation is not reflexive , symmetric and not transitive . Hence it is not an equivalence relation.