100 CHAPTER 2 Formal Logic
(a) (p A q A r) --> s
(b) (t A u) -- v
(c) -s -) -'v
(d) p A (q A r) V (t A u) V (--S V --V)
(e) ((p V t) A (q v u)) +-+ (S A V)One must sometimes be a bit creative in using language to make the results compre-
hensible.- Let p denote the proposition "Jill plays basketball" and q denote the proposition "Jim
plays soccer." Write out-in the clearest way you can-what the following proposi-
tions mean:
(a) -'p
(b) p A q
(c) pvq(d) -pAq
(e) p --+ q
(f) p *q
(g) --q -_ p- Let p denote the proposition "Sue is a computer science major" and q denote the
proposition "Sam is a physics major." Write out what the following propositions mean:
(a) -q
(b) q A p
(c) pvq
(d) -q A p
(e) q - p
(f) p÷-q
(g) -q -+ p- Jim, George, and Sue belong to an outdoor club. Every club member is either a skier
or a mountain climber, but no member is both. No mountain climber likes rain, and all
skiers like snow. George dislikes whatever Jim likes and likes whatever Sue dislikes.
Jim and Sue both like rain and snow. Is there a member of the outdoor club who is a
mountain climber? - Let proposition p be T and proposition q be F. Find the truth values for the following:
(a) pvq
(b) q A p
(c) -p V q
(d) p A -q
(e) q -+ p
(f) -p -q
(g) -q -- p - Let proposition p be T, proposition q be F, and proposition r be T. Find the truth
values for the following:
(a) pvqvr
(b) p v (-q A -r)
(c) p ---. (q V r)