Question -
Answer -
Given R ={(a, b): b = a + 1}
Now for this relationwe have to check whether it is reflexive, transitive and symmetric Reflexivity:
Let a be an arbitraryelement of R.
Then,a = a + 1 cannot be true for all a ∈ A.
⇒ (a, a) ∉ R
So, R is not reflexive on A.
Symmetry:
Let (a, b) ∈ R
⇒ b = a + 1
⇒ −a = −b + 1
⇒ a = b − 1
Thus, (b, a) ∉ R
So, R is not symmetric on A.
Transitivity:
Let (1, 2) and (2, 3) ∈ R
⇒ 2 = 1 + 1 and 3
2 + 1 is true.
But 3 ≠ 1+1
⇒ (1, 3) ∉ R
So, R is not transitive on A.