For problems $1-3,$ assume $$ is defined as the first order language with the logical symbols and punctuation of FOL but has the following non$-$logical symbols:

a$,$ b$,$ P$1,$ f$2$

where a and b are constants, P$1$ is a unary predicate, and f$2$ is a binary function.

$1.$ Using $$ from above:

$($a$)5$ points. Construct two different terms of $.$

$($b$)5$ points. Construct two different atomic formulas of $.$

$($c$)5$ points. Using the atomic formulas from $($b$),$ construct two compound $($i$.$e$.$ non$-$atomic$)$ formulas of$$