Let R and S be two non-void relations on a set A. Which of the following statements is false?

JEE Main Mathematics question

Let and be two non-void relations on a set . Which of the following statements is false?

(A) and are transitive implies is transitive
(B) and are transitive implies is transitiveCorrect
(C) and are symmetric implies is symmetric
(D) and are reflexive implies is reflexive

Answer: (B)

Solution

Check (B) with a counter-example. Let , and . Each of and is transitive (there is no chain to break). But contains the chain while is missing, so the union

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Question ID VK-007342