VERIFIED ANSWERS
FFTF.
In order for a conjunction to be true, both conjuncts must be true. If one of the
conjuncts is a negation, like "-p," then the sentence that is negated (in this case, p)
has to be false in order for the conjunct "-p" to be true. So the conjunction "-iPAQ"
is only true when p is false and q is true. - CORRECT ANSWER Suppose you had to
fill in the rightmost column of the truth table below:
p q -iPAQ
TT
TF
FT
FF
Going from top to bottom, how would you fill in that column?
TTTF
In order for a conditional to be false, the antecedent must be true and the
consequent must be false. If the antecedent is a negation, like -p, then the
sentence that is negated (in this case, p) has to be false for the antecedent to be
true. So the conditional "-p⊃q" is only false when p is false and q is false, and it is
true otherwise. - CORRECT ANSWER Suppose you had to fill in the rightmost
column of the truth table below:
,p q -p⊃q
TT
TF
FT
FF
Going from top to bottom, how would you fill in that column?
FFFFTFFF
In order for a conjunction to be true, both conjuncts must be true. In order for a
negation to be true, the sentence, which is being negated, must be false. So for
the conjunction "-p&(q&r)" to be true, p must be false, q must be true, and r must
be true. This is the only assignment on which the whole conjunction can be true.
Otherwise, it is false. - CORRECT ANSWER Suppose you had to fill in the rightmost
column of the truth table below:
p q r -p&(q&r)
TTT
TTF
TFT
TFF
FTT
FTF
,FFT
FFF
Going from top to bottom, how would you fill in that column?
-p
Given a conjunction, one can infer either of its conjuncts. So, from the conjunction
-p&q, one can infer -p and one can infer q. Both -p and q follow from -p&q. None
of the other options among (a)-(d) follow, however. - CORRECT ANSWER Which of
these claims follows from -p&q?
none of the above.
From a conditional, and nothing else, one cannot infer its antecedent, nor can one
infer its consequent. One can only infer the consequent if the premises include
both the conditional and its antecedent, and one can only infer the negation of
the antecedent if the premises include both the conditional and the negation of
the consequent. Since all we have is the conditional, none of (a)-(d) follow. -
CORRECT ANSWER Which of these claims follows from -p⊃q?
-p - CORRECT ANSWER Which of these claims follows from -p&(q&r)?
FFFFFFFT
c) is correct. In order for the rightmost conjunction to be true, both of its
conjuncts have to be true. This means that -r has to be true, which requires r to be
false. It also requires -(pVq) to be true, which requires pVq to be false. The only
way for a disjunction to be false, however, is for both its disjuncts to be false. So,
in order for the rightmost conjunction to be true, p, q, and r ALL have to be false.
, Otherwise, the rightmost conjunction is false. - CORRECT ANSWER Suppose you
had to fill in the rightmost column of the following truth-table:
p q r pVq -(pVq) -r -(pVq)&-r
TTT
TTF
TFT
TFF
FTT
FTF
FFT
FFF
Going from top to bottom, how would you fill it in?
FFFTFTFT
(c) is correct. In order for the rightmost proposition to be true, the disjunction of
(p&q)Vr has to be false. A disjunction is false, however, only when both of its
disjuncts is false. For both of the disjuncts of (p&q)Vr to be false, however, r has to
be false, and at least one p or q has to be false, too. (This is because the first
disjunct, p&q, is a conjunction, which is false when either one of its conjuncts is
false.) So, in order for the rightmost conjunction to be true, both r and either p or
q must be false. So if r is true, or if both p and q are true, then the rightmost
proposition is false. Otherwise, the rightmost proposition is true. - CORRECT
ANSWER Suppose you had to fill in the rightmost column of the following truth-
table: