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

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Question 3:

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**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.

*a*,

*b*):

*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 = {(

*a*,*b*):*b*=*a*+ 1}
∴R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}

We can find (

*a*,*a*) ∉ R, where*a*∈ 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.