CSE 20: Discrete Mathematics
Spring 2010
Problem Set 1
Instructor: Daniele Micciancio
Due on:
Thu. April 8, 2010
Problem 1 (6 points)
Write down a parenthesized version of each of the following boolean formulas according to the standard
precedence rules of boolean algebra:
1.
¬
P
∨
Q
→
P
∧
R
2.
P
→
Q
∨ ¬
R
∧
S
∧
P
→
Q
3.
A
∨
B
∧
C
∧ ¬
D
→
A
Problem 2 (10 points)
For each of the following pairs of propositional formulas, determine if they are equivalent or not using the
truth table method. Your solution should include (for each equivalence) the corresponding truth table and
a brief sentence stating if the given equivalence is valid (or not) and why.
1.
(
A
→
B
)
∧
(
A
∨
B
)
≡
B
2.
(
A
→
B
)
∧
(
B
→
C
)
→
(
C
→
A
)
≡
A
Problem 3 (10 points)
Complete the following proof of the equivalence
(
¬
q
→
r
)
→
r
≡
q
→
r
justifying each line with the name
of the algebraic rule applied to it, and underlining the subformula the rule has been applied to.
(As an
example, the answer for the first step if provided.) You can use any rule from Theorem 2 from the textbook
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 Fall '08
 Foster
 Boolean Algebra, Boolean function, Logical connective, Propositional calculus

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