s=Tuples[{a,b},{2,2}]

Make a set of matrices

s2=MatrixForm/@s

find a subset

subset=RandomChoice@Subsets[s2]

find the complement

Complement[s2,subset]

Make a mixed  set

s={,,(({{a, a}, {b, a}})),ToString@N@Pi, ψ,,ToString[(∫_m^n)Φ("λ")\[DifferentialD]"λ",TraditionalForm],,Plot3D[{x^2+y^2,-x^2-y^2},{x,-2,2},{y,-2,2},RegionFunction->Function[{x,y,z},x^2+y^2≤4],BoxRatios->Automatic]}

get a suset

subset=RandomChoice@Subsets[s]

find complement

Complement[s,subset]

s=Union[Range[9], RandomSample[Subsets[Range[5]],4]]
s2=Subsets[s];

RandomChoice@s2

random set

rand=Union[Range[9], RandomSample[Subsets[Range[5]],4]]

SubsetQ[s,rand]
SubsetQ[s,RandomChoice@s2]

s={{"∅"}};
s2=Subsets[s]/.{{}->"∅"}

Subsets[s2]/.{{}->"∅"}

s=Range[2]

s2=Subsets[s]/.{{}->"∅"}

Subsets[s2]/.{{}->"∅"}

Subsets[{}]/.{{}->"∅"}