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Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as ...

Check whether the relation R defined in | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

Question: 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.

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.

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Popular questions of class 12 Mathematics

Q: Given an example of a relation. Which is
(i) Symmetric but neither reflexive nor transitive.
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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , 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 re....

Check whether the relation R defined in | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

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