Login/Sign Up
Let A = {1, 2, 3, 4, 5, 6) and let R = {(a, b) : a, b ∈ A and b = a + 1}. Show that R is (i) not transitive.
Let A = {1, 2, 3, 4, 5, 6) and let R = {(a, b) : a, b ∈ A and b = a + 1}. Show that R is
(i) not transitive.
CBSE | Class 12 | Exercise 1A | Maths | Relations | RS Aggarwal
Let A = {1, 2, 3, 4, 5, 6) and let R = {(a, b) : a, b ∈ A and b = a + 1}. Show that R is
(i) not transitive.

Solution:

(i) Non-transitive:
If $p, q$ and $r \in A$ such that $(p, q) \in R$ and $(q, r) \in R \Rightarrow(p, r) \in R$, then $\mathrm{R}$ is transitive.
Here, $(1,2) \in \mathrm{R}$ and $(2,3) \in \mathrm{R}$ but $(1,3) \notin \mathrm{R}$
As a result, $R$ is not transitive.

i

More Material