Prove the following predicates are decidable knowing that $A$ and $B$ are decidable predicates: $$\lnot A$$ $$A \lor B$$
I am supposed to prove this by writing a program or using some other way that a predicate is decidable but I am not sure how to do that.
You have to use at least an "abstract" model of algorithm.
Assume that you have a "machine" - call it $M_A$ - which, receiving as input one object $x$ in your domain of discourse in turn, after a finite amount of time stops and gives you the answer YES if $A$ holds for that object $x$, and NO if $A$ does not hold for $x$.
Now, having $M_A$, we can easily build up the $M_{\lnot A}$ "machine" : "run" the $M_A$ machine with input $x$ and , when it stops and ouput YES, then "add" a new instruction which translate the output into NO (and vice versa). This is the new "machine" $M_{\lnot A}$.