CmSc 175 Discrete Mathematics
Name:
Homework 04: due 02/08 by midnight
Please record the time it takes to solve each problem and write it down after the problem. Save the file as your_first_nameHW04.doc and upload to Scholar. Thank you.
1. Re-write as conditionals and then write the negations of the following sentences (20 pts)
a. Students cannot register for classes unless they are approved by their advisor
b. Passing this course is sufficient for me to graduate
c. To enjoy downhill skiing it is necessary to have snow
d. Being a spider is sufficient for being disliked
e. I am able to wake up in the morning only if I drink three cups of coffee.
2. Which of the following sentences are equivalent to
“He is a Martian only if he has six legs”
Underline the correct answers. (12 pts)
a. If one is a Martian then one has six legs.
b. If you don’t have 6 legs you are not a Martian
c. If you are not a Martian you don’t have six legs
d. If one has 6 legs then one is a Martian
e. You are not a Martian unless you have six legs
f. You don’t have six legs unless you are a Martian
3. Given the premises below show that u L w is true (18 pts)
p ® q (1)
r V s (2)
~q V s (3)
~s (4)
~p L r ® u (5)
w V~ r (6)
4. For each sentence below do the following:
a. Write the quantified predicate expression using the given predicates and the quantifiers $ and "
b. Negate the expression
c. Translate the negated expression in English
(18 pts)
1. No students that participate in the debate will be able to attend the workshop
student(x), participate_debate(x), attend_workshop(x)
Expression:
Negation:
Translation:
2. Employees that work after hours will be compensated
employee(x), work(x), compensated(x)
Expression:
Negation:
Translation:
3. Some students that are in the Dean’s list will attend the meeting
student(x), Dean’s_list(x), attend_meeting(x)
Expression:
Negation:
Translation:
5. Determine whether the following arguments are valid or invalid. If valid determine the type of argument. If invalid determine the type of error if the type is known.
(32 pts)
a. All lawyers are wealthy Valid Invalid
All wealthy people eat lobster
\ All lawyers eat lobster
b. Some lawyers are wealthy Valid Invalid
Some doctors are wealthy
\ Some lawyers are doctors
c. All doctors like music Valid Invalid
All poets like music
\ All doctors are poets
d. Some doctors are intelligent Valid Invalid
All intelligent people like music
\ Some doctors like music
e. All men like red meat Valid Invalid
Some teachers are men
\ Some teachers like red meat
f. All men are mortal Valid Invalid
Geese are not men
\ Geese are not mortal
g. All cars are expensive Valid Invalid
Bicycles are not expensive
\ Bicycles are not cars
h. All teachers watch TV Valid Invalid
Some kids watch TV
\ Some kids are teachers
1