what could be the answer of a compound proposition with 3 variables

Question

I don't know how I could answer the truth table of $(p \lor q \lor ¬r) \land (p \lor ¬q \lor ¬s) $ because it's kind of confusing because it has 3 variables in one parentheses and I want some specific and clarified answer.

Answer 1

Because disjunction is associative you have $(p \vee q ) \vee \lnot r=p \vee (q \vee \lnot r)$. To construct the truth table for this you would have $2^3=8$ lines, one for each of the possible combinations of truth values of $p,q,r$. Because of the associativity you can make a column with $p \vee q$ and then with $(p \vee q) \vee \lnot r$. You should find seven true values and one false value. When you add in the other conjunct you need $2^4$ lines because you have a fourth variable.