Solutions16

# Solutions16 - Chapter 16 Hints and Selected Solutions...

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Chapter 16: Hints and Selected Solutions Section 16.1 (page 449) 16.3 You are asked to give two distinct derivations of the ambig-wff 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 ambig-wff. Hence, by the induction clause, ¬ A 2 is an ambig-wff. Then, using the induction clause again, A 2 ↔ ¬ A 2 is an ambig-wff. By the basis clause, A 1 is an ambig-wff. Using the induction clause again gives us that A 1 A 2 ↔ ¬ A 2 is an ambig-wff. 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).

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