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Quizzes

Quiz #1, 10/8

Symbolize the following sentences in SL. Make sure to give a key showing what you mean by each of the sentence letters.

Check to see: Are the sentences equivalent? Are they consistent?

(1) Unless those creatures are men in suits, they are either chimpanzees or they are gorillas.
(2) If those creatures are chimpanzees, then they are neither gorillas nor men in suits.

Answer:

Note, of course, that there are other possible symbolizations.

M: They are men in suits.
C: They are chimpanzees.
G: They are gorillas.

M v (C v G)
C (G v M)

If C, G, and M were all true, then (1) would be true while (2) was false. Thus, there is a truth value assignment on which (1) and (2) have different truth values. They aren't equivalent.

If C were true but G and M were false, then both (1) and (2) would be true. Thus, there is a truth value assignment on which both are true. They are consistent.

Quiz #2, 10/13

Symbolize the following sentences in PL.

UD: the 3 animals Amos, Bouncer, and Cleo
Ax: x is an alligator
Mx: x is a monkey
Rx: x is a reptile
Zx: x lives at the zoo
Lxy: x loves y
a: Amos
b: Bouncer
c: Cleo

(1) Amos, Bouncer, and Cleo all live at the zoo.
(2) Bouncer is a reptile, but not an alligator.
(3) If Cleo loves Bouncer, then Bouncer is a monkey.
(4) If both Bouncer and Cleo are alligators, then Amos loves them both.

(1) Za & Zb & Zc
or: (x) Zx
(2) Rb & ~Ab
(3) Lcb Mb
(4) (Ab & Ac) (Lab & Lac)

Quiz #3, 10/20

UD: animals
Ax: x is an alligator
Mx: x is a monkey
Rx: x is a reptile
Zx: x lives at the zoo

(1) Some reptile lives at the zoo.
(2) Every alligator is a reptile.
(3) Any animal that lives at the zoo is either a monkey or an alligator.
(4) There are reptiles which are not alligators.

(1) (x) (Rx & Zx)
(2) (x) (Ax Rx)
(3) (x) [Zx (Mx v Ax)]
(4) (x) (Rx & ~Ax)