Section 1.3 Quantifiers, Predicates, and Validity
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g. No bee loves only flowers.
j. Every bee hates some flowers.
h. Some bees love some flowers.
k. Every bee hates all flowers.
i. Some bees love only flowers.
l. No bee hates all flowers.
24. Using the predicate symbols shown and appropriate quantifiers, write each English language statement as
a predicate wff. (The domain is the whole world.)
S(x): x is a spy novel
L(x): x is long
M(x): x is a mystery
B(x, y): x is better than y
a. All spy novels are long.
b. Not every mystery is a spy novel.
c. Only mysteries are long.
d. Some spy novels are mysteries.
e. Spy novels are better than mysteries.
f. Some mysteries are better than all spy novels.
g. Only spy novels are better than mysteries.
25. Give English language translations of the following wffs if
L(x, y): x loves y
H(x): x is handsome
M(x): x is a man
P(x): x is pretty
W(x): x is a woman
j: John
k: Kathy
L(x, y): x loves y
a. H( j) ` L(k, j)
b. (4x)[M(x) S H(x)]
c. (4x)(W(x) S (4y)[L(x, y) S M( y) ` H( y)])
d. (E x)[M(x) ` H(x) ` L(x, k)]
e. (E x)(W(x) ` P(x) ` (4y)[L(x, y) S H( y) ` M( y)])
f. (4x)[W(x) ` P(x) S L( j, x)]
26. Give English language translations of the following wffs if
M(x): x is a man
W(x): x is a woman
i: Ivan
p: Peter
W(x, y): x works for y
a. (E x)(W(x) ` (4y)(M( y) S [W(x, y)]′))
b. (4x)[M(x) S (E y)(W( y) ` W(x, y))]
c. (4x)[M(x) S (4y)(W(x, y) S W( y))]