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Home » 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.
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.
CBSE | Class 12 | Exercise 1.1 | Maths | NCERT | Relations and Functions
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.

solution:

R = {(a, b) : b = a + 1}

R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}

At the point when b = a, a = a + 1: which is bogus, So R isn’t reflexive.

In the event that (a, b) = (b,a), b = a+1 and a =b+1: Which is bogus, so R isn’t symmetric.

Presently, in the event that (a, b), (b,c) and (a, c) has a place with R

b = a+1 and c =b+1 which infers c = a + 2: Which is bogus, so R isn’t transitive. Consequently, R is neither reflexive, nor symmetric and nor transitive.

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