Question

the binary relation S=∅ on set A={1,2,3} is transitive and symmetric

Answer 1

Defintion of symmetric relation.. here X is a set and a,b are elements of X

Defintion of transitive relation.. here X is a set and a,b and c are elements of X


Now if you see given relation S=ϕ
There are no elements in the set, so it does not violate the definitions of the symmetric and transitive realtions above..
Hence it is symmetric and transitive.

Extra:
But the given relation is not reflexive...
in a reflexive relation, for every element a of set X, aRa.
but here we donot have 1R1 and 2R2 and 3R3.
So, the given relation S=ϕ is not reflexive

Comments

in fact the smallest symmetric and transitive relation is ϕ.

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Aha, NPTEL IIT MADRAS.