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MACM 101 — Discrete Mathematics I, Fall 2010
Assignment 1.
Due: Friday, September 24 (at the beginning of class)
Reminder: the work you submit must be your own. Any collaboration and
consulting outside resourses must be explicitly mentioned on your submission.
Please, use a pen. 30 points will be taken oﬀ for pencil written work.
1. Construct a truth table for the following compound proposition:
(
¬
p
↔ ¬
q
)
↔
(
q
↔
r
).
2. Show that the following compound statement is a contradiction
((
p
→
q
)
∨
(
p
→
r
))
⊕
(
p
→
(
q
∨
r
))
.
3. Show that (
p
↔
q
) and (
¬
p
↔ ¬
q
) are logically equivalent.
4. Show that (
p
∧
q
)
→
r
and (
p
→
r
)
∧
(
q
→
r
) are not logically equivalent. Do not use
truth tables.
5. Simplify the compound statement
¬
(
p
∨
q
∨
(
¬
p
∧¬
q
∧
r
))
.
6. Prove that the Rule of Disjunctive Syllogism is a valid argument.
7. For each of these sets of premises, what relevant conclusion or conclusions can be
drawn? Explain the rules of inference used to obtain each conclusion from the premises.
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 Summer '08
 PEARCE

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