In this question, assume the following predicate and constant symbols:

W(x,y) : x wrote y

L(x,y) : x is longer than y

N(x) : x is a novel

h : Hardy

a : Austen

j : Jude the Obscure

p : Pride and Predjudice

Given these specifications, which of the predicate logic formulas below represent the sentence,

- x (W(h,x) L(x,a)))
- x y (L(x,y) W(h,y) W(a,x))
- x y (W(h,x) W(a,y) L(x,y)))
- x (N(x) W(h,x) y (N(y) W(a,y) L(x,y)))
- x y (W(h,x) W(a,y) L(x,y))

In this question, assume the following predicate and constant symbols.

W(x,y) : x wrote y

L(x,y) : x is longer than y

h : Hardy

a : Austen

j : Jude the Obscure

p : Pride and Predjudice

Which of the following represents the sentence,

Working with a unary predicate sysmbol, P, a binary predicate symbol Q and a unary function sysmbol f, which of the following formulas are satisfied in the model M, given by,

A = {a,b,c,d};

P

Q

f

Which of the following sets of sentences is satisfiable? (Recall that a "sentence" is a predicate logic formula that has no free variables.)

- { x Q(x), x (Q(x) R(x)), x R(x)}.
- { y x P(x,y), x P(x,x)}.
- { x y (P(x,y) P(y,y)), x P(x,x), x y (P(x,y)}.
- { x y P(x,y), x P(x,x)}.
- { x Q(x), x Q(x)}.

Which of the following semantic entailments are valid in predicate logic?

- x (P(x) Q(x)) x P(x) x Q(x)
- x (P(x) Q(x)) x P(x) x Q(x)
- x P(x) x Q(x) x (P(x) Q(x))
- x (P(x) Q(x)) x P(x) x Q(x)
- x P(x) x Q(x) x (P(x) Q(x))

In this question assume the specifications

F(x,y) : x is the father of y

M(x,y) : x is the mother of y.

Which of the formulas in predicate logic below express the sentence

In this question assume only the specifications

F(x,y) : x is the father of y

M(x,y) : x is the mother of y.

Which of the formulas in predicate logic below express the sentence

- x ( y F(x, y) y z (M(x, y) M(y, z)))
- x ( y F(x, y) y M(x, M(y)))
- x ( y F(x, y) y G(x, y))
- x y F(x, y) x y M(x, y)
- x (F(x) M(M(x)))

For this question and the following one, assume the specifications below:

The predicate symbols

S(x,y) : x is y's sister

B(x,y) : x is y's brother

H(x,y) : x is y's husband and

O(x,y) : x is older than y

and the constant symbols

j : John,

c : Carl, and

m : Monique.

Which of the following formulas express the sentence

- B(c,m) H(c,m).
- B(c,m) H(c,m).
- x y (S(x,m) H(c,y) x = y).
- x ((S(x,m) H(c,x)) (H(x,m) B(c,x))).
- None of the above.

Assuming the same specifications as for Question 8, which of the following sentences are expressed by the predicate logic formula

x y (S(x,j) S(y,j) O(x,y))?.

- John has an older sister.
- All of John's sisters are older than him.
- John is older than his sisters.
- One of John's sisters is older than another.
- None of the above.

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