From Mathematical Structures for Computer Science, 7th edition by Gersting: 1.1

Question

From Mathematical Structures for Computer Science, 7th edition by Gersting:

1.1 38. You want your program to execute statement 1 when A is false, B is false, and C is true, and to execute statement 2 otherwise. You wrote

if not(A and B) and C then
   statement 1
else
   statement 2
end if

Does this do what you want?

1.3 4. What is the truth value of each of the following offs in the interpretation where the domain consists of the real numbers?
a. (-/x(3y)(x = y^2)       c. (3x)(-/y)(x = y^2)
b. (-/x)(-/y)(x = y^2)   d. (3x)(3y)(x = y^2)

16. Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff.

A(x): x is an animal
B(x): x is a bear
H(x): x is hungry
W(x): x is a wolf
a. Bears are animals.
b. No wolf is a bear.
c. Only bears are hungry.
d. If all wolves are hungry, so are bears.
e. Some animals are hungry bears.
f. Bears are hungry but some wolves are not.
g. If wolves and bears are hungry, so are all animals.
h. Some wolves are hungry but not every animal is hungry.

22. Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff.

C(x): x is a Corvette
F(x): x is a Ferrari
P(x): x is a Porsche
S(x, y): x is slower than y
a. Nothing is both a Corvette and a Ferrari.
b. Some Porsches are slower than only Ferraris.
c. Only Corvettes are slower than Porsches.
d. All Ferraris are slower than some Corvettes.
e. Some Porsches are slower than no Corvette.
f. If there is a Corvette that is slower than a Ferrari, then all Corvettes are slower than all Ferraris.

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
a. (3x)(W(x) / (-/y)(M(y) -> [W(x, y)]’))
b. (-/x)[M(x) -> (3y)(W(y) / W(x, y))]
c. (-/x)[M(x) -> (-/y)(W(x, y) -> W(y))]
d. (-/x)(-/y)(M(x) / W(y, x) -> W(y))
e. W(i, p) / (-/x)[W(p, x) -> (W(x))’])
f. (-/x)[W(x, i) -> (W(x))’]

28. Three forms of negation are given for each statement. Which is correct?
a. Nobody is perfect.
   1. Everyone is imperfect.
   2. Everyone is perfect.
   3. Someone is perfect.
b. All swimmers are tall.
   1. Some swimmer is not tall.
   2. There are no tall swimmers.
   3. Every swimmer is short.
c. Every planet is cold and lifeless.
   1. No planet is cold and lifeless.
   2. Some planet is not cold and not lifeless.
   3. Some planet is not cold or not lifeless.
d. No bears are hungry.
   1. Only bears are hungry.
   2. All bears are hungry.
   3. There is a hungry bear.

30. Write the negation of each of the following statements.
   a. only students eat pizza.
   b. Every student eats pizza.
   c. Some students eat only pizza.

Explanation / Answer

1.1.38.

It is provided that the variable A is false, B is false and C is false. The if statement should be changed such that if the statement becomes true, the statement 1 will be executed. If the statement becomes false, the statement 2 will be executed.

The following is the changes that should be made in the if statement and it is provided as follows:

if not (A and B) or C then

     statement 1

else

     statement 2

end if

28.

a.

Let P(x) denotes x is perfect such that

The statement “Nobody is perfect” is expressed as

The negation of the expression is as follows:

Therefore, the negation of the given statement “Nobody is perfect” is option 3 “Someone is perfect”.

b.

Let x denotes a swimmer and P(x) denotes that the swimmer is tall.

The statement “All swimmers are tall” is expressed as .

The negation of the expression is as follows:

Therefore, the negation of the given statement “All swimmers are tall” is option 1 “Some swimmer is not tall”.

c.

Let x be a planet, P(x) states that the planet is cold and Q(x) states that the planet is lifeless.

The statement “Every planet is cold and lifeless” is expressed as .

The negation of the expression is as follows:

Therefore, the negation of the given statement “Every planet is cold and lifeless” is option 3 “Some planet is not cold or not lifeless”.

d.

Let x be a bear and P(x) states that the bear is hungry.

The statement “No bears are hungry” is expressed as .

The negation of the expression is as follows:

Therefore, the negation of the given statement “No bears are hungry” is option 3 “There is a hungry bear”.

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.