[(pvqvr) -> (p^q^r)] <--> [((pvq) -> r) ^ (r -> (p^q))]
How would I separate the variables out into columns? How many columns would there be? Please explain in basic detail as I would not be able to understand advanced Baring in mind my key:
v = OR
^ = AND
-> = Implication
<--> = Exclusive
I'll assume, since you mentioned columns, that you're trying to produce the truth table of your formula. Your truth table should begin with three columns, labeled $p$, $q$, and $r$. In these columns, enter all of the possible combinations of truth values for these three variables. So you'll have 8 rows. Then put additional columns in which you calculate (in each of the 8 rows) the truth values of the other formulas involved in your problem: $p\lor q$, $p\lor q\lor r$, $p\land q$, $p\land q\land r$, $$ (p\lor q\lor r)\to(p\land q\land r), $$ $$ (p\lor q)\to r,\qquad r\to(p\land q), $$ $$ ((p\lor q)\to r)\land (r\to(p\land q)), $$ and finally $$ [(p\lor q\lor r)\to(p\land q\land r)]\leftrightarrow [((p\lor q)\to r)\land (r\to(p\land q))]. $$