Prove that the relation ‘’Superset of ’’ is a partial order relation on the power set of S.

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solution : yes it is partial order

because it follow the three property

a)Reflexive

b)Antisymmetric

c)Transitive

Reflexive: $A⊇A$ It is reflexive (any set s is a superset of itself)

Antisymmetric:the only time both $A⊇B$ and $B⊇A$ is when A=B(superset is antisymmetric)

Transitive: $A⊇B$ and $B⊇C$ $\implies$ $A⊇C$ (SUPERSET is transitive)