GATE | GATE-CS-2009 | Question 4

Consider the binary relation R = {(x, y), (x, z), (z, x), (z, y)} on the set {x, y, z}. Which one of the following is TRUE?
(A) R is symmetric but NOT antisymmetric
(B) R is NOT symmetric but antisymmetric
(C) R is both symmetric and antisymmetric
(D) R is neither symmetric nor antisymmetric

Answer: (D)

Explanation: R is not symmetric as (x, y) is present, but (y, x) is not present in R.

R is also not antisymmetric as both (x, z) and (z, x) are present in R.

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