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Solution


Q.

The number of relations, on the set {1, 2, 3} containing (1, 2) and (2, 3), which are reflexive and transitive but not symmetric, is _________ .               [2023]

Ans.

(3)

Let we have set A={1,2,3}

By definition, we can say that

For reflexivity: (1,1),(2,2),(3,3)∈R  ...(i)

For symmetry: (2,1),(1,2)∈R  ...(ii)

For transitivity: (1,2)∈R and (2,3)∈R⇒(1,3)∈R  ...(iii)

But according to the question,

For not symmetric: (2,1) and (3,2)∉R  ...(iv)

So, R1={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}

R2={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(2,1)}

and R3={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(3,2)}