CSE 20: Discrete Mathematics
Fall 2011
Problem Set 2
Instructor: Daniele Micciancio
Due on:
Wed. October 12, 2011
This homework assignment is based on Sections 1.2 and 1.3 of the textbook.
Problem 1 (12 points)
In class we proved (using the truth table method) that the following derivation rule (called “proof by cases”)
is valid: if
p
∨
q
,
p
→
r
and
q
→
r
are all true, then
r
is also true. (In symbols, (
p
∨
q
)
,
(
p
→
r
)
,
(
q
→
r
) =
⇒
r
.)
In this problem, you will give a formal proof sequence that “proof by cases” is a valid derivation rule.
Complete the following proof sequence for the inference (
p
∨
q
)
,
(
p
→
r
)
,
(
q
→
r
) =
⇒
r
by providing a
justiﬁcation for each line. The justiﬁcation should include the name of the derivation rule used, and the line
numbers of the statements it is applied to. As justiﬁcation you can use any of the equivalence rules in Table
1.3 or inference rules in Table 1.4 at page 1819 of the textbook, as well as “given” and the “distributive
property”
p
∨
(
q
∧
r
)
≡
(
p
∨
q
)
∧
(
p
∨
r
) from Exercise 1.1, 14(b) on page 11. (As an example of proof sequences
with justiﬁcations, see Examples 1.7, 1.8 and 1.9 in the textbook.)
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 Spring '08
 Foster
 Logic, Proof theory, proof sequence, derivation rule

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