1. Exploring Partially ordered sets
Ordered by the subset relation

2. 3: Pow({a,b,c})
{a,b,c}
{a,b}
{b,c}
{a,c}
{a}
{b}
{c}
{Ø}

3. 4: Pow({a,b,c,d}) {a,b,c,d} 1x4 4x3 {b,c,d} {a,c,d} {a,b,d} {a,b,c}
{a,d}
{b,c}
{a,c}
{a,b}
4x2
4x1
{d}
{c}
{b}
{a}
1x0
{Ø}

4. 5: Pow({a,b,c,d,e}) {a,b,c,d,e} 1X5 {b,c,d,e} {a,c,d,e} {a,b,d,e}
{a,b,c,e}
{a,b,c,d}
5X4
{c,d,e}
{b,d,e}
{b,c,e}
{b,c,d}
{a,d,e}
{a,c,e}
{a,c,d}
{a,b,e}
{a,b,d}
{a,b,c}
10X3
{d,e}
{c,d}
{b,d}
{a,d}
{a,c}
{c,e}
{b,c}
{b,e}
{a,e}
{a,b}
10X2
{e}
{d}
{c}
{b}
{a}
5X1
1X0
{Ø}

5. 6: Pow({a,b,c,d,e,f}) {a,b,c,d,e,f} 1X6 {b,c,d,e,f} {a,c,d,e,f}
{a,b,d,e,f}
{a,b,c,e,f}
{a,b,c,d,f}
{a,b,c,d,e}
6X5
15X4
{c,d,e,f}
{b,d,e,f}
{b,c,e,f}
{b,c,d,f}
{b,c,d,e}
{a,d,e,f}
{a,c,e,f}
{a,c,d,f}
{a,c,d,e}
{a,b,e,f}
{a,b,d,f}
{a,b,d,e}
{a,b,c,f}
{a,b,c,e}
{a,b,c,d}
{d,e,f}
{c,e,f}
{c,d,f}
{c,d,e}
{b,e,f}
{b,d,f}
{b,d,e}
{b,c,f}
{b,c,e}
{b,c,d}
{a,e,f}
{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}
20X3
{e,f}
{d,f}
{c,f}
{d,e}
{c,e}
{c,d}
{b,f}
{b,e}
{b,d}
{b,c}
{a,f}
{a,e}
{a,d}
{a,c}
{a,b}
15X2
6X1
{f}
{e}
{d}
{c}
{b}
{a}
1X0
{Ø}

6. 7: Pow({a,b,c,d,e,f,g}) {a, b, c, d, e, f, g} 1X7 {b, c, d, e, f, g}
{a, c, d, e, f, g}
{a, b, d, e, f, g}
{a, b, c, e, f, g}
{a, b, c, d, f, g}
{a, b, c, d, e, g}
{a, b, c, d, e, f}
7X6
{c, d, e, f, g}
{b, d, e, f, g}
{b, c, e, f, g}
{b, c, d, f, g}
{b, c, d, e, g}
{b, c, d, e, f}
{a, d, e, f, g}
{a, c, e, f, g}
{a, c, d, f, g}
{a, c, d, e, g}
{a, c, d, e, f}
{a, b, e, f, g}
{a, b, d, f, g}
{a, b, d, e, g}
{a, b, d, e, f}
{a, b, c, f, g}
{a, b, c, e, g}
{a, b, c, e, f}
{a, b, c, d, g}
{a, b, c, d, f}
{a, b, c, d, e}
21X5
{d, e, f, g}
{c, e, f, g}
{c, d, f, g}
{c, d, e, g}
{c, d, e, f}
{b, e, f, g}
{b, d, f, g}
{b, d, e, g}
{b, d, e, f}
{b, c, f, g}
{b, c, e, g}
{b, c, e, f}
{b, c, d, g}
{b, c, d, f}
{b, c, d, e}
{a, e, f, g}
{a, d, f, g}
{a, c, f, g}
{a, d, e, g}
{a, d, e, f}
{a, c, e, g}
{a, c, e, f}
{a, c, d, g}
{a, c, d, f}
{a, c, d, e}
{a, b, f, g}
{a, b, e, g}
{a, b, e, f}
{a, b, d, g}
{a, b, d, f}
{a, b, d, e}
{a, b, c, g}
{a, b, c, f}
{a, b, c, e}
{a, b, c, d}
35X4
{e, f, g}
{d, f, g}
{d, e, g}
{d, e, f}
{c, f, g}
{c, e, g}
{c, e, f}
{c, d, g}
{c, d, f}
{c, d, e}
{b, f, g}
{b, e, g}
{b, e, f}
{b, d, g}
{b, d, f}
{b, d, e}
{b, c, g}
{b, c, f}
{b, c, e}
{b, c, d}
{a, f, g}
{a, e, g}
{a, e, f}
{a, d, g}
{a, d, f}
{a, d, e}
{a, c, g}
{a, c, f}
{a, c, e}
{a, c, d}
{a, b, g}
{a, b, f}
{a, b, e}
{a, b, d}
{a, b, c}
35X3
{f,g}
{e, g}
{e, f}
{d, g}
{d, f}
{d, e}
{c, g}
{c, f}
{c, e}
{c, d}
{b, g}
{b, f}
{b, e}
{b, d}
{b, c}
{a, g}
{a, f}
{a, e}
{a, d}
{a, c}
{a, b}
21X2
{g}
{f}
{e}
{d}
{c}
{b}
{a}
7X1
1X0
{Ø}

7. 7: Pow(Pow{a,b,c})) {{a,b,c}, {b,c}, {a,c}, {a,b}, a, b, c} {c} {b}
{{a,b,c}, {a,c}, {a,b}, a, b, c}
{{a,b,c}, {b,c}, {a,b}, a, b, c}
{{a,b,c}, {b,c}, {a,c}, a, b, c}
{{a,b,c}, {b,c}, {a,c}, {a,b}, b, c}
{{a,b,c}, {b,c}, {a,c}, {a,b}, a, c}
{{a,b,c}, {b,c}, {a,c}, {a,b}, a, b}
{{a,c}, {a,b}, a, b, c}
{{b,c}, {a,b}, a, b, c}
{{b,c}, {a,c}, a, b, c}
{{b,c}, {a,c}, {a,b}, b, c}
{{b,c}, {a,c}, {a,b}, a, c}
{{b,c}, {a,c}, {a,b}, a, b}
{{a,b,c}, {a,b}, a, b, c}
{{a,b,c}, {a,c}, a, b, c}
{{a,b,c}, {a,c}, {a,b}, b, c}
{{a,b,c}, {a,c}, {a,b}, a, c}
{{a,b,c}, {a,c}, {a,b}, a, b}
{{a,b,c}, {b,c}, a, b, c}
{{a,b,c}, {b,c}, {a,b}, b, c}
{{a,b,c}, {b,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}, {b,c}, {a,c}, a, c}
{{a,b,c}, {b,c}, {a,c}, a, b}
{{a,b,c}, {b,c}, {a,c}, {a,b}, c}
{{a,b,c}, {b,c}, {a,c}, {a,b}, b}
{{a,b,c}, {b,c}, {a,c}, {a,b}, a}
{{a,b}, a, b, c}
{{a,c}, a, b, c}
{{a,c}, {a,b}, b, c}
{{a,c}, {a,b}, a, c}
{{a,c}, {a,b}, a, b}
{{b,c}, a, b, c}
{{b,c}, {a,b}, b, c}
{{b,c}, {a,b}, a, c}
{{b,c}, {a,b}, a, b}
{{b,c}, {a,c}, b, c}
{{b,c}, {a,c}, a, c}
{{b,c}, {a,c}, a, b}
{{b,c}, {a,c}, {a,b}, c}
{{b,c}, {a,c}, {a,b}, b}
{{b,c}, {a,c}, {a,b}, a}
{{a,b,c}, a, b, c}
{{a,b,c}, {a,b}, b, c}
{{a,b,c}, {a,c}, b, c}
{{a,b,c}, {a,b}, a, c}
{{a,b,c}, {a,b}, a, b}
{{a,b,c}, {a,c}, a, c}
{{a,b,c}, {a,c}, a, b}
{{a,b,c}, {a,c}, {a,b}, c}
{{a,b,c}, {a,c}, {a,b}, b}
{{a,b,c}, {a,c}, {a,b}, a}
{{a,b,c}, {b,c}, b, c}
{{a,b,c}, {b,c}, a, c}
{{a,b,c}, {b,c}, a, b}
{{a,b,c}, {b,c}, {a,b}, c}
{{a,b,c}, {b,c}, {a,b}, b}
{{a,b,c}, {b,c}, {a,b}, a}
{{a,b,c}, {b,c}, {a,c}, c}
{{a,b,c}, {b,c}, {a,c}, b}
{{a,b,c}, {b,c}, {a,c}, a}
{{a,b,c}, {b,c}, {a,c}, {a,b}}
{a, b, c}
{{a,b}, b, c}
{{a,b}, a, c}
{{a,b}, a, b}
{{a,c}, b, c}
{{a,c}, a, c}
{{a,c}, a, b}
{{a,c}, {a,b}, c}
{{a,c}, {a,b}, b}
{{a,c}, {a,b}, a}
{{b,c}, b, c}
{{b,c}, a, c}
{{b,c}, a, b}
{{b,c}, {a,b}, c}
{{b,c}, {a,b}, b}
{{b,c}, {a,b}, a}
{{b,c}, {a,c}, c}
{{b,c}, {a,c}, b}
{{b,c}, {a,c}, a}
{{b,c}, {a,c}, {a,b}}
{{a,b,c}, b, c}
{{a,b,c}, a, c}
{{a,b,c}, a, b}
{{a,b,c}, {a,b}, c}
{{a,b,c}, {a,b}, b}
{{a,b,c}, {a,b}, a}
{{a,b,c}, {a,c}, c}
{{a,b,c}, {a,c}, b}
{{a,b,c}, {a,c}, a}
{{a,b,c}, {a,c}, {a,b}}
{{a,b,c}, {b,c}, c}
{{a,b,c}, {b,c}, b}
{{a,b,c}, {b,c}, a}
{{a,b,c}, {b,c}, {a,b}}
{{a,b,c}, {b,c}, {a,c}}
{b,c}
{a, c}
{a, b}
{{a,b}, c}
{{a,b}, b}
{{a,b}, a}
{{a,c}, c}
{{a,c}, b}
{{a,c}, a}
{{a,c}, {a,b}}
{{b,c}, c}
{{b,c}, b}
{{b,c}, a}
{{b,c}, {a,b}}
{{b,c}, {a,c}}
{{a,b,c}, c}
{{a,b,c}, b}
{{a,b,c}, a}
{{a,b,c}, {a,b}}
{{a,b,c}, {a,c}}
{{a,b,c}, {b,c}}
{c}
{b}
{a}
{{a,b}}
{{a,c}}
{{b,c}}
{{a,b,c}}
{Ø}