Answer to Question #238445 in Discrete Mathematics for Lapace

Question

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

Answer 1

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.