Constructing A Truth Table

Question

How do I construct a truth table with a formula that has 3 logical operators that lack a parentheses? $$P \lor Q \land \neg(R \lor \neg S)$$

Under "~" you mean negation? "V" is "or"? "Λ" is "and"? – zkutch Aug 03 '20 at 01:34 — zkutch, Aug 03 '20 at 01:34
Yes negation is ~ and V is or and Λ is and – Gerome Tahud Aug 03 '20 at 01:40 — Gerome Tahud, Aug 03 '20 at 01:40
I inserted formatting - is it now what you asked about? – zkutch Aug 03 '20 at 01:42 — zkutch, Aug 03 '20 at 01:42

score 1 · Accepted Answer · answered Aug 03 '20 at 01:46

1

Generally $$P \lor Q \land \neg(R \lor \neg S)$$ is same as $$P \lor (Q \land (\neg(R \lor (\neg S))))$$ Can you proceed now?

answered Aug 03 '20 at 01:46

zkutch

13,410

Thanks man this is all I need. – Gerome Tahud Aug 03 '20 at 01:47

score 0 · Answer 2 · answered Aug 03 '20 at 01:41

0

You need to establish where the parentheses are to make a truth table. The truth values of $P \vee (Q \wedge R)$ and $(P \vee Q) \wedge R$ can be different. Maybe your environment has a standard for whether $\vee$ binds tighter than $\wedge$, in which case you know. If not, you don't. I don't know what is standard, but I assume they are equal and parentheses are needed.

answered Aug 03 '20 at 01:41

Ross Millikan

374,822

Thanks for the info. The only hint i got was "be mindful of the precedence of logical operators". – Gerome Tahud Aug 03 '20 at 01:44
The precedence would be which operator binds more tightly. I don't know which one does for your class. If $\wedge$ binds more tightly you should read it as the first of my examples. – Ross Millikan Aug 03 '20 at 01:50

Constructing A Truth Table

2 Answers2