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

The **Answer to the Question**

is below this banner.

**Here's the Solution to this Question**

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.