# Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.A. R is reflexive and symmetric but not transitive.B. R is reflexive and transitive but not symmetric.C. R is symmetric and transitive but not reflexive.D. R is an equivalence relation.A. R is reflexive and symmetric but not transitive.B. R is reflexive and transitive but not symmetric.C. R is symmetric and transitive but not reflexive.D. R is an equivalence relation.

It is given that the relation in the set {1, 2, 3, 4} given by

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

Check symmetric:

As (1,1),(2,2),(3,3),(4,4) ϵ R

It is seen that (a, a) ϵ R, for every a ϵ {1,2,3,4}

Therefore, R is reflexive.

Check symmetric:

We can seen that (1, 2) ϵ R, but (2, 1) R.

Therefore, R is not symmetric.

Check transitive:

(a, b), (b, c) ϵ R

(a, c) ϵ R

here (1,3) ϵ R , (3,2) ϵ R and (1,2) ϵ R

Therefore, R is transitive.

Therefore, R is reflexive and transitive but not symmetric.

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