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Home » Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.
Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.
CBSE | Class 12 | Exercise 1.1 | Maths | NCERT | Relations and Functions
Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

solution:

R = {(1, 2), (2, 1)}

(x, x) ∉ R. R isn’t reflexive.

(1, 2) ∈ R and (2,1) ∈ R. R is symmetric.

Once more, (x, y) ∈ R and (y, z) ∈ R then, at that point (x, z) doesn’t suggest to R. R isn’t transitive. Thusly, R is symmetric however neither reflexive nor transitive.

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