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McMaster University
Department of Computing and Software
Dr. W. Kahl
COMP SCI 1FC3
Sheet 4
COMP SCI 1FC3 — Mathematics for Computing
26 January 2012
Exercise 4.1
Prove Identity of
∨
(3.30),
p
∨
false
≡
p
, by transforming its more structured side into its simpler side. Theorem
(3.15) may be a suitable way to introduce an equivalence.
Exercise 4.2
Prove the following using the heuristic of DeFnition elimination (3.23) — eliminate
∧
(using its deFnition, the
Golden rule (3.35),
p
∧
q
≡
p
≡
q
≡
p
∨
q
) and manipulate.
(a) Prove Symmetry of
∧
(3.36),
p
∧
q
≡
q
∧
p
(b) Prove Zero of
∧
(3.40),
p
∧
false
≡
false
Exercise 4.3
(a) Prove Contradiction (3.42)
p
∧¬
p
≡
false
(b) Prove Absorption (3.43a)
p
∧
(
p
∨
q
)
≡
p
(c) Prove Absorption (3.43b)
p
∨
(
p
∧
q
)
≡
p
(d) Prove Distributivity of
∨
over
∧
(3.45)
p
∨
(
q
∧
r
)
≡
(
p
∨
q
)
∧
(
p
∨
r
)
Exercise 4.4 — Ladies or Tigers: The First Trial —
Will be discussed in the Wednesday lecture
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This note was uploaded on 02/06/2012 for the course COMP SCI 1FC3 taught by Professor Kahlwolfram during the Spring '11 term at McMaster University.
 Spring '11
 KahlWolfram

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