Q1) What is the truth value of each of the following statements in the interpretation where the domain consists of the integers, A(x) is x<5 and B(x) is x<7?

a) (x)A(x)

b) (x)[A(x) B(x)]

c) (x)[A(x) -> B(x)]

d) (x)[B(x) -> A(x)]

Q2) For the statement below, find an interpretation in which it is true and one in which it is false.

(x)[A(x) (y)B(x, y)]

True:

False:

Q3) Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate statement. (The domain is the whole world.)

B(x): x is a ball.

R(x): x is round.

S(x): x is a soccer ball

a) All balls are round.

b) Not all balls are soccer balls.

c) All soccer balls are round.

d) Some balls are not round.

e) Some balls are round but soccer balls are not.

Q4) Give English language translations of the following statements 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) (x)(W(x) (y)(M(y) -> [W(x, y)]))

b) W(i, p) (x)[ W(p, x) -> (W(x))]

Q5) Three forms of negation are given for the following statement. Which is correct?

"Nobody is perfect."

a) Everyone is imperfect.

b) Everyone is perfect.

c) Someone is perfect.

Q6) Three forms of negation are given for the following statement. Which is correct?

"All swimmers are tall."

a) Some swimmer is not tall.

b) There are no tall swimmers.

c) Every swimmer is short.

Q7) Prove by contraposition that if n is an integer and 3n + 2 is even, then n is even.

Q8) Prove by contradiction that if n is an integer and 3n + 2 is even, then n is even.