Chapter 16: Hints and Selected Solutions
Section 16.1 (page 449)
16.3
You are asked to give two distinct derivations of the ambigwﬀ
A
1
→
A
2
↔ ¬
A
2
. Here is one. You should be able to think of another. By the
basis clause,
A
2
is an ambigwﬀ. Hence, by the induction clause,
¬
A
2
is
an ambigwﬀ. Then, using the induction clause again,
A
2
↔ ¬
A
2
is an
ambigwﬀ. By the basis clause,
A
1
is an ambigwﬀ. Using the induction
clause again gives us that
A
1
→
A
2
↔ ¬
A
2
is an ambigwﬀ.
16.7
Hint: Consider the word
noon
. Is it a palindrome? Is it a pal?
Section 16.2 (page 453)
16.12
The set
S
of wﬀs is the smallest set satisfying the following clauses:
1. Each propositional letter is in
S
.
2. If
p
is in
S
, then sois
¬
p
.
3. If
p
and
q
are in
S
, then so are (
p
∧
q
)
,
(
p
∨
q
)
,
(
p
→
q
)
,
and (
p
↔
q
).
16.13
Hint: Your proof will have a basis case, corresponding to clause (1)
and an inductive case, corresponding to clauses (2) and (3). There will
be one case for clause (2) and four for clause (3).
Section 16.3 (page 455)
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 Spring '09
 dhoe
 Logic, Mathematical Induction, Natural number, Mathematical logic, induction step

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