Question

Let P be the power set of {a, b, c}. Draw the diagram of the partial order induced on P by the lattice (P,(,().

Answer 1

Let $P=\{\emptyset,\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a, b, c\}\}$ be the power set of $\{a, b, c\}$. Let us draw the diagram of the partial order induced on $P$ by the lattice $(P,\subseteq):$

Note that in this diagram we draw $A\to B$ if $A\subseteq B.$