Question 3: Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is reflexive, symmetric or transitive. Chapter 1 - Relations And Functions

Chapter 1 - Relations And FunctionsNCERT Solutions for Class 12 Science Math

Question 3:

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} asR = {(ab): b = a + 1} is reflexive, symmetric or transitive.

ANSWER:

Let A = {1, 2, 3, 4, 5, 6}.
A relation R is defined on set A as:
R = {(ab): b = a + 1}
∴R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}
We can find (aa) ∉ R, where ∈ A.
For instance, 
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) ∉ R
∴R is not reflexive.
It can be observed that (1, 2) ∈ R, but (2, 1) ∉ R.
∴R is not symmetric.
Now, (1, 2), (2, 3) ∈ R
But, 
(1, 3) ∉ R
∴R is not transitive 
Hence, R is neither reflexive, nor symmetric, nor transitive.

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