Solutions07

# Solutions07 - a Large e 16 Tet c Cube b 19 Large a Small d...

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Chapter 7: Hints and Selected Solutions Section 7.2 (page 183) 7.2 The truth table for this Exercise is shown below. Since all the entries in the main columns for each sentence are the same, row by row, the sentences are tautologically equivalent. 7.5 The truth table for this Exercise is shown below. The entries in the main columns for each sentence are not the same. They each have one False and the rest Trues, but the Falses come in diﬀerent rows. Hence the sentences are not tautologically equivalent. 1

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7.12 1. Tet ( a ) FrontOf ( a , d ) 4. Small ( c ) RightOf ( c , a ) 7. Tet ( e ) ( ¬ FrontOf ( b , d ) → ¬ BackOf ( b , d )) 10. Cube ( a ) Cube ( c ) Cube ( e ) 13. Larger ( a , c ) Larger ( e , c ) ∧ ¬ ( Large
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Unformatted text preview: ( a ) Large ( e )) 16. Tet ( c ) Cube ( b ) 19. Large ( a ) Small ( d ) 7.16 Hint: All of the sentences are important, but probably the biggest clue comes from the sentence FrontOf ( a , b ) ( FrontOf ( b , c ) FrontOf ( c , b )). Section 7.4 (page 194) 7.25 2. ( Tet ( a ) Small ( a )) 2 6. ( Tet ( a ) Small ( a )) ( Tet ( a ) Small ( a )) 7.29 We can express P using the Sheer stroke as P | P . Examination of the truth table for | shows that P | P is false when P is true and true when P is false. 3...
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Solutions07 - a Large e 16 Tet c Cube b 19 Large a Small d...

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