Solutions10

# Solutions10 - Chapter 10 Hints and Selected Solutions...

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Unformatted text preview: Chapter 10: Hints and Selected Solutions Section 10.1 (page 264) 10.1 The following fills in some of the rows for you. Be sure you understand these. Annotated sentence Truth-functional form a/b/c 1. ∀ x ( x = x ) A A b 4. ∀ x ( Cube ( x ) ∧ Small ( x )) A → ∀ x ( Small ( x ) ∧ Cube ( x )) B A → B b 7. [ ∀ z ( Cube ( z ) → Large ( z )) A ∧ Cube ( b ) B ] → Large ( b ) C [ A ∧ B ] → C b 10 [( ∀ u Cube ( u ) A → ∀ u Small ( u )) B ∧ ¬∀ u Small ( u ) B ] → ¬∀ u Cube ( u ) A [( A → B ] ∧ ¬ B ] → ¬ A a 10.2 The argument is logically valid, but its truth functional form is as shown below, so it is not tautologically valid. (We have not shown the anno- tation, but you should be able to figure it out from the form.) A ∧ B C ∧ D E ∧ F 10.4 The argument is tautologically valid. Here is its truth functional form: A → B ¬ B ¬ A 1 Section 10.2 (page 273) 10.8 10.9 The second sentence is not a logical truth. It is false in many worlds....
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Solutions10 - Chapter 10 Hints and Selected Solutions...

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