Exploring
Partially ordered sets
Ordered by the subset relation
3: Pow({a,b,c})
{a,b,c}
{a,b}
{a}
{a,c}
{b}
{Ø}
{b,c}
{c}
4: Pow({a,b,c,d})
{a,b,c,d}
{a,c,d}
{b,c,d}
{c,d}
{d}
{b,d}
1x4
{a,b,d}
{a,d}
{b,c}
{c}
{a,b,c}
{a,c}
{b}
{a,b}
{a}
4x3
4x2
4x1
1x0
{Ø}
5: Pow({a,b,c,d,e})
{a,b,c,d,e}
{b,c,d,e}
{c,d,e}
{d,e}
{b,d,e}
{c,d}
{e}
{a,c,d,e}
{b,c,e}
{b,c,d}
{b,d}
{a,d}
{d}
1X5
{a,b,d,e}
{a,d,e}
{a,c}
{c}
{Ø}
{a,b,c,e}
{a,b,c,d}
5X4
{a,c,e}
{a,c,d}
{a,b,e}
{a,b,d}
{a,b,c}
10X3
{c,e}
{b,c}
{b,e}
{a,e}
{a,b}
10X2
{b}
{a}
5X1
1X0
6: Pow({a,b,c,d,e,f})
{a,b,c,d,e,f}
{b,c,d,e,f}
{c,d,e,f}
{b,d,e,f}
{a,c,d,e,f}
{b,c,e,f}
{a,b,d,e,f}
{b,c,d,f} {b,c,d,e} {a,d,e,f} {a,c,e,f}
{d,e,f} {c,e,f} {c,d,f} {c,d,e {b,e,f} {b,d,f} {b,d,e}
}
{e,f}
{d,f}
{c,f}
{d,e}
{c,e}
{b,c,f} {b,c,e
}
{c,d}
{b,f}
1X6
{a,b,c,e,f}
{a,c,d,f}
{a,c,d,e} {a,b,e,f}
{b,c,d} {a,e,f}
{b,e}
{a,b,c,d,f}
{b,d}
{a,b,d,f}
{a,b,c,d,e}
{a,b,d,e} {a,b,c,f}
6X5
{a,b,c,e} {a,b,c,d}
{a,d,f} {a,d,e} {a,c,e} {a,c,f} {a,c,d} {a,b,f} {a,b,e} {a,b,d} {a,b,c}
{b,c}
{a,f}
{a,e}
{a,d}
{a,c}
15X4
20X3
{a,b}
15X2
6X1
{f}
{e}
{d}
{c}
{b}
{a}
1X0
{Ø}
7: Pow({a,b,c,d,e,f,g})
{a, b, c, d, e, f, g}
{b, c, d, e, f, g}
{c, d, e, {b, d, e,
f, g}
f, g}
{d,
e,
f,
g}
{e,
f, g}
{c,
e,
f,
g}
{d,
f, g}
{c,
d,
f,
g}
{c,
d,
e,
g}
{d, {d,
e, g} e, f}
{b, c, e,
f, g}
{c,
d,
e,
f}
{b,
e,
f,
g}
{c, f, {c,
g}
e,
g}
{f,g}
{e, g}
{a, c, d, e, f, g}
{b, c, d,
f, g}
{b, c, d,
e, g}
{b,
d,
f,
g}
{b,
d,
e,
g}
{c,
e, f}
{c,
d, g}
{e, f}
{g}
{b,
d,
e,
f}
{b, c, d,
e, f}
{b,
c,
f,
g}
{c,
d, f}
{a, d, e,
f, g}
{b,
c,
e,
g}
{c,
d, e}
{d, g} {d, f}
{f}
{a, b, d, e, f, g}
{b,
c,
e,
f}
{b,
f, g}
{a, c, e,
f, g}
{b,
c,
d,
g}
{a, c, d,
f, g}
{b,
c,
d,
f}
{b,
{b,
e, g} e, f}
{b,
c,
d,
e}
{b,
d,
g}
{d, e} {c, g} {c, f}
{e}
1X7
{a, b, c, e, f, g}
{a, c, d,
e, g}
{a,
e,
f,
g}
{b,
d, f}
{c, e}
{a,
d,
f,
g}
{b,
d, e}
{a, b, e,
f, g}
{a, c, d,
e, f}
{a,
c,
f,
g}
{a,
d,
e,
g}
{b,
{b,
c, g} c, f}
{c, d}
{d}
{Ø}
{a, b, c, d, f, g}
{a,
d,
e,
f}
{b,
c, e}
{a, b, d,
f, g}
{a, b, d,
e, g}
{a,
c,
e,
g}
{a,
c,
e,
f}
{b,
c, d}
{a,
f, g}
{b, g} {b, f} {b, e}
{c}
{a, b, c, d, e, g}
{a, b, d,
e, f}
{a, b, c,
f, g}
{a,
c,
d,
g}
{a,
c,
d,
f}
{a,
c,
d,
e}
{a,
b,
f,
g}
{a,
e, g}
{a,
e, f}
{a,
d, g}
{a,
d, f}
{b, d}
{b, c}
{a, g}
{b}
{a, b, c,
e, g}
{a,
b,
e,
g}
{a,
d, e}
{a, f}
{a,
b,
e,
f}
{a,
c, g}
{a, b, c, d, e, f}
{a, b, c,
e, f}
{a, b, c,
d, g}
{a,
b,
d,
g}
{a,
b,
d,
f}
{a,
{a,
c, f} c, e}
{a, e} {a, d}
{a}
{a,
c, d}
7X6
{a, b, c,
d, f}
{a,
b,
d,
e}
{a,
b,
c,
g}
{a,
{a,
b, g} b, f}
{a, c} {a, b}
{a, b, c,
d, e}
{a,
b,
c,
f}
{a,
b,
e}
21X5
{a,
b,
c,
e}
{a,
b,
c,
d}
35X4
{a, {a,
b, d} b, c}
35X3
21X2
7X1
1X0
7: Pow(Pow{a,b,c}))
{{a,b,c}, {b,c}, {a,c}, {a,b}, a, b, c}
{{b,c},
{a,c},
{a,b}, a,
b, c}
{{a,c}, {{b,c},
{a,b}, a, {a,b}, a,
b, c}
b, c}
{{a,b} {{a,c} {{a,c}
, a, b, , a, b, ,
c}
c}
{a,b},
b, c}
{{a,c}
,
{a,b},
a, c}
{{b,c},
{a,c}, a,
b, c}
{{a,c} {{b,c}
,
, a,
{a,b}, b, c}
a, b}
{a, b, {{a,b {{a,b {{a,b {{a,c {{a,c
c}
}, b, }, a, }, a, }, b, }, a,
c}
c}
b}
c}
c}
{b,c}
{a, c}
{{a,b,c},
{a,c},
{a,b}, a,
b, c}
{{b,c},
{a,c},
{a,b}, b,
c}
{{b,c}
,
{a,b},
b, c}
{{b,c},
{a,c},
{a,b}, a,
c}
{{b,c}
,
{a,b},
a, c}
{{b,c}
,
{a,b},
a, b}
{{a,c} {{a,c}
, a,
,
b}
{a,b},
c}
{a, b}
{c}
{{a,b},
c}
{{a,b,c},
{b,c},
{a,b}, a,
b, c}
{{b,c},
{a,c},
{a,b}, a,
b}
{{b,c}
,
{a,c},
b, c}
{{a,c
},
{a,b}
, b}
{{a,b,c},
{a,b}, a,
b, c}
{{b,c}
,
{a,c},
a, c}
{{b,c}
,
{a,c},
a, b}
{{a,b,c},
{a,c}, a,
b, c}
{{b,c}
,
{a,c},
{a,b},
c}
{b}
{{a,b},
a}
{{a,c},
c}
{{a,b,c},
{a,c},
{a,b}, b,
c}
{{b,c}
,
{a,c},
{a,b},
b}
{{a,c} {{b,c {{b,c} {{b,c}
,
}, b, , a, , a,
{a,b}, c}
c}
b}
a}
{{a,b},
b}
{{a,b,c},
{b,c},
{a,c}, a,
b, c}
{{b,c
},
{a,b}
, c}
{{a,c},
b}
{a}
{{a,b,c},
{a,c},
{a,b}, a,
c}
{{a,b,c},
{b,c},
{a,c},
{a,b}, b,
c}
{{b,c} {{a,b, {{a,b, {{a,b,
c}, a, c},
,
c},
{a,c}, b, c} {a,b}, {a,c},
b, c} b,
{a,b},
a}
c}
{{b,c
},
{a,b}
, b}
{{a,c},
a}
{{b,c}
,
{a,b},
a}
{{a,b,c},
{b,c}, a,
b, c}
{{a,b,c},
{a,c},
{a,b}, a,
b}
{{b,c}
,
{a,c},
c}
{{a,c},
{a,b}}
{{a,b,
c},
{a,b},
a, b}
{{b,c}
,
{a,c},
b}
{{b,c}
,
{a,c},
a}
{{b,c},
c}
{{b,c},
b}
{{a,b}}
{Ø}
{{a,b,
c},
{a,b},
a, c}
{{a,b,c},
{b,c},
{a,b}, b,
c}
{{a,b,
c},
{a,c},
a, c}
{{a,b,c},
{b,c},
{a,b}, a,
c}
{{a,b,
c},
{a,c},
a, b}
{{b,c} {{a,b
,
,c},
{a,c}, b, c}
{a,b}
}
{{b,c},
a}
{{a,b,c},
{b,c},
{a,c},
{a,b}, a,
c}
{{a,b,c},
{b,c},
{a,b}, a,
b}
{{a,b,c},
{b,c},
{a,c}, b,
c}
{{a,b,
c},
{a,c},
{a,b},
c}
{{a,b,
c},
{a,c},
{a,b},
b}
{{a,b,
c}, a,
c}
{{a,b, {{a,b, {{a,b
c}, a, c},
,c},
b}
{a,b}, {a,b}
c}
, b}
{{b,c},
{a,b}}
{{a,c}}
{{b,c},
{a,c}}
{{a,b,
c},
{a,c},
{a,b},
a}
{{a,b,
c},
{b,c},
b, c}
{{a,b,c},
c}
{{a,b,c},
{b,c},
{a,c},
{a,b}, a,
b}
{{a,b,c},
{b,c},
{a,c}, a,
c}
{{a,b,
c},
{b,c},
a, c}
{{a,b,
c},
{a,b},
a}
{{a,b,c},
b}
{{b,c}}
{{a,b,c},
{b,c},
{a,c}, a,
b}
{{a,b,
c},
{b,c},
a, b}
{{a,b,
c},
{a,c},
c}
{{a,b,c},
{b,c},
{a,c},
{a,b}, c}
{{a,b,
c},
{b,c},
{a,b},
c}
{{a,b,
c},
{a,c},
b}
{{a,b,
c},
{b,c},
{a,b},
b}
{{a,b
,c},
{a,c},
a}
{{a,b,c}, {{a,b,c},
a}
{a,b}}
{{a,b
,c},
{a,c},
{a,b}
}
{{a,b,c},
{b,c},
{a,c},
{a,b},
b}
{{a,b,
c},
{b,c},
{a,b},
a}
{{a,b,
c},
{b,c},
c}
{{a,b,
c},
{b,c},
{a,c},
c}
{{a,b,
c},
{b,c},
b}
{{a,b,c}, {{a,b,c},
{a,c}}
{b,c}}
{{a,b,c}}
{{a,b,c},
{b,c},
{a,c},
{a,b},
a}
{{a,b,
c},
{b,c},
{a,c},
b}
{{a,b
,c},
{b,c},
a}
{{a,b,
c},
{b,c},
{a,c},
a}
{{a,b,
c},
{b,c},
{a,b}
}
{{a,b,
c},
{b,c},
{a,c},
{a,b}}
{{a,b,
c},
{b,c},
{a,c}}