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