[AGuzman26]

#5 what does the symbol you used mean/represent? is it the Null symbol?

[Suman Ganguli]

That symbol φ is the Greek letter “phi”–think of it as a variable which is meant to represent any compound proposition of propositional logic.

Actually, if it’s helpful, the questions could be rewritten as follows, without using the symbol (but then the questions get wordier–which is the main reason we use symbols in math!):

(a) Write down, in terms of its truth table, definitions of what it means for a compound proposition to be:
-a tautology
-a satisfiable
-unsatisfiable

(b) Prove that if a given compound proposition is unsatisfiable, then the negation of that proposition is a tautology.