Question

Let A be a given finite set and P(A) its power set. Let ⊆ be the inclusion relation on the elements of P(A). Draw Hasse diagrams of (P(A), ⊆) for A={a}; A={a,b}; A={a,b,c} and A={a,b.c.d}.

Answer 1

for $A=\{a\}$ :

$P(A)=\{\empty,\{a\}\}$

for $A=\{a,b\}$ :

$P(A)=\{\empty,\{a\},\{b\},\{a,b\}\}$

for $A=\{a,b,c\}$ :

$P(A)=\{\empty,\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\}$

for $A=\{a,b,c,d\}$ :

$P(A)=\{\empty,\{a\},\{b\},\{c\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},$

$\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\}$