UGC-NET Computer Science July 2016 Solved Paper 2

Q:2 Suppose that R1 and R2 are reflexive relations on a set A.

Which of the following statements is correct ?

(A) R1∩R2 is Reflexive and R1∪R2 is irreflexive

(B) R1∩R2 is irReflexive and R1∪R2 is reflexive

(C) Both R1∩R2 and R1∪R2 are reflexive

(D) Both R1∩R2 and R1 ∪R2 are irreflexive

Answer: C

Explanation:

Suppose if both R1 and R2 are Reflexive, Symmetric and Transitive i.e. R1 and R2 are both equivalence relations then:

R1∩R2 is Reflexive, Symmetric and Transitive.

R1∪R2 is Reflexive, Symmetric but not Transitive.

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