If there are two prop vars, p and q. as you mentioned, we check for true case and false case for only one var because it covers every possible case in the truth table, so checking for other var also is redundant. For equival we see if truth values both sides are same, and for tauto, we see if we get lhs T and rhs F in any of the two cases. If there are more vars, we might have to repeat case method.