- #1
BubblesAreUs
- 43
- 1
Since I'm not sure if posting assignment questions is allowed, I'm just going to ask specific questions just to be safe.
1. Homework Statement
Find all the lower bounds of given pair. Say (a, b) in T.
Proof for greatest lower bound:
∀g,a,b ∈ T ⇔ ( g ≺ a) ^ (g ≺ b) ^ ( ∀l ∈ T [ (l ≺ a ) ^ ( l ≺ b)] ⇒ (l ≺ g)
by "≺", I meant Partial Order, ≤
Since g are ordered before a and b. Can we assume for pair {2, 4}, g will be equivalent to
{empty set}, {1,0}, {1,1}, {1,2}, {1,3}, {1,4}, {2, 1}, {2,2}, {2,3}, {2,4},
I am not sure if I'm on the right track, but that's what it seems to be according to the proof.
1. Homework Statement
Find all the lower bounds of given pair. Say (a, b) in T.
Homework Equations
Proof for greatest lower bound:
∀g,a,b ∈ T ⇔ ( g ≺ a) ^ (g ≺ b) ^ ( ∀l ∈ T [ (l ≺ a ) ^ ( l ≺ b)] ⇒ (l ≺ g)
by "≺", I meant Partial Order, ≤
The Attempt at a Solution
Since g are ordered before a and b. Can we assume for pair {2, 4}, g will be equivalent to
{empty set}, {1,0}, {1,1}, {1,2}, {1,3}, {1,4}, {2, 1}, {2,2}, {2,3}, {2,4},
I am not sure if I'm on the right track, but that's what it seems to be according to the proof.