CS 281 Solutions to Test I

June 3, 1997

1. (a) or
(b)
(c) or
(d)
(e)

2. (a)
(b)
(c)
(d)
(e) .

3 (a) Converse: If I can't complete the task, then I don't get more help.
Contrapositive: If I can complete the task, then I get more help.
(b) Converse: If you go, then I will stay.
Contrapositive: If you don't go, then I will not stay.
(c) Converse: If you get an A in Math 101, then you get(got) 95 in the final.
Contrapositive: If you don't get an A in Math 101, then you don't(didn't) get 95 in the final.
(d) Converse: If you get an A in the final, then you get an A in Math 101.
Contrapositive: If you don't get an A in the final, then you don't get an A in Math 101.

4. Let W: Today is Wednesday.
C: I have a quiz in Computer Science.
M: I have a quiz in Math 101.
S: My Math professor is sick.

(a) W C M
S M
W S
----------------
C

(b) Step (1):
W S W (Simplification)
W S
----------------
W

Step (2):
W C M (Premise)
W
----------------
C M

Step (3):
W S S (Simplification)
W S
----------------
S

Step (4):
S M (Premise)
S
----------------
M

Step (5):
C M (From Step (2))
M
----------------
C

(c) The argument is correct because the conclusion (C) is derived from the premises by applying the modus ponens.

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