Consider the following PL sentence: $(($P & $$Q$)($Q & $$P$))$

a$)$ What is the scope of the first occurrence of conjunction in this sentence?

$($b$)$ What is the scope of the second occurrence of negation in this sentence?

$($c$)$ What is the main operator of this sentence?

$($d$)$ Show the formation process for this sentence, either as a list of steps or as a $$flowchart$.$

$($e$)$ Provide a complete truth table for this sentence. Circle the main operator column.

$($f$)$ Determine the logical status of this sentence: tautology, contradiction, or contingency?

$($g$)$ Explain your answer to part $($f$)$ by referring to your truth table and showing how the

definition of the relevant concept $($tautology$,$ contradiction, or contingency$)$ applies to

this sentence.