Ok, first and foremost:
V represents OR.
^ represents AND.
=> for condional.
Just wanted to point that out since I don't have the actual symbols on my keyboard and don't know how to get them.
I was doing some revision on predicates and came accross this question:
Show that:
[ (p => q)^(q => r) ] => (p => r) = 1
I changed the equation to this:
[ (p ^ -q) V (q ^ -r) ] V (-p V r) = 1
But what do I do with the 1? How does the one relate to the equation?
I don't remember coming accross this in my lectures.
As you realized, $1$ is often used to denote $true$, and $0$ denotes $false$. This isn't arbitrary, because $x \land y = x \times y$ with real arithmetic! Additionally, we use bitmasks with $1$ denoting presence of some property and $0$ denoting absence.