Show that the power set of S={a,b,c} is a poset under set inclusion

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Solution:

Given, S={a,b,c}

Assume A is a subset of power set of S.

Reflexivity: A ⊆ A whenever A is a subset of S.

Antisymmetry: If A and B are positive integers with A ⊆ B and B ⊆ A, then A = B.

Transitivity: If A ⊆ B and B ⊆ C, then A ⊆ C

Thus, the power set of S={a,b,c} is a poset under set inclusion(⊆).

Hence, proved.