Simple Steps for how to make a truth table for all interpretations of
a formula in Propositional Logic:
An Interpretation is an assignment of truth values (T or F) to the atomic
components of a compound formula.
Consider the formula: ~ ( B & A )
In Englis

TRUTH TABLE FOR AN ARGUMENT
Recall the earlier example of a compound formula:
C ~(Q v A)
Now, lets take that formula and make it the premise of an argument form:
1. C
~ ( Q v A ) If Chuck plays, then it is false that Quin or Al will play
2. ~A & ~Q
Al won

STYLISTIC VARIANTS of English for Truth-Functional Statements
Conditional: P Q
If antecedent then consequent
If Peter wins, then Quincy weeps.
Quincy weeps if Peter wins.
Peter wins only if Quincy weeps.
Peter wins implies that Quincy weeps.
Peter winning

How to make a truth table for formulas that have 3 atomic statements
Consider, for example, the compound formula:
C ~(Q v A)
In English, this might read as:
If Charlie plays soccer, then neither Quincy nor Alice will play or, equally,
Charlie plays soccer