Glb and Lub in a lattice diagram

Question

Given the following lattice, what is the pair $(c \wedge e, d \vee b)?$

I know that $c \wedge e=0$.

But is $d \vee b=d$ or $d \vee b=1$? I don't really understand it.

($\wedge,\vee$ represent glb,lub)

Answer 1

• Write all the elements that are $\geq b$: $\{b,d,e,1\}$
• Write all the elements that are $\geq d$: $\{d,1\}$

What is the lowest upper bound? If you look at both sets you conclude that is the element $d$.

Answer 2

Since b < d < 1, how could 1 be the least upper bound of {b,d}?