Problem Set $3$

PHIL $11\mathrm{.}4$

Pxoblem Set #$3$

$(10$ points$)$ Using only the procedure I showed you in class, specify an

interpretation for each of the following sentences of LSL making it true:

a$)(P$&$Q)$&$((R$notP$)$&$(Q$notR$))$

$(b)not(Q((P$&$)(RharrS)))$

$(18$ points$)$ Use truth tables to determine which of the following sentences

are logically equivalent. To do so$,$ set up the base columns for $P$ and $Q($in

alphabetic order$)$ once, line up the truth$-$tables for the sentences, and

then determine which of the sentences are equivalent to each other. Please

indicate your answer:

$($a$)QP$

$($b$)$ PvvnotQ

$($c$)$ notQvv$(notQvvP)$

$($d$)$ notQ & $P$

$($e$)$ not$(notP$&$Q)$

$($f$)(PharrnotQ)(QP)$