Let L={a,b,c,d,e,f}, P(L) is power set of L and
≤
is order relation on P(L) defined as:

if r and t are relations, then
r≤t
iff every block in r is subset of some block in t. Show that lattice
(P(L),≤)
is not modular.

Question

Let L={a,b,c,d,e,f}, P(L) is power set of L and  
≤
 is  order relation on P(L) defined as:

if r and t are relations, then 
r≤t
 iff every block in r is subset of some block in t.   Show that lattice 
(P(L),≤)
 is not modular.

jamesj · Answer

What's the definition of modular here?

gg · Answer

wait a second

gg · Answer

lattice (L,∨,∧) is modular if a ≤ c implies a ∨ (b ∧ c) = (a ∨ b) ∧ c.

gg · Answer

I know to draw Hasse diagram, but I don't know what t do after. Maybe to try to find N5?

anonymous · Answer

Gg try to ask this question here http://math.stackexchange.com/

gg · Answer

can u check this:
let 
    r2={{a,b}, {c}, {d}, {e}, {f}}
    r3={{c,d,e}, {a}, {b}, {f}}
    r4={{a,b,c,d}, {e}, {f}}
    r5={{a,b,c,d,f}, {e}}
    r6={{a,b,c,d,e,f}}

is |dw:1323201799967:dw|    N5 (penthagon) ?