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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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- Spring '09