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303a5solns

# 303a5solns - ASSIGNMENT 5 SOLUTIONS MATH 303 FALL 2011 If...

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ASSIGNMENT 5 SOLUTIONS MATH 303, FALL 2011 If you ﬁnd any errors please let me know. Manipulation (M1) w y ( x = ( w,y )) you could also expand out more if you want . (M2) (1 point) Which of the following are well formed formulas and which of the well formed ones are good? (a) Not well formed ( 3 is not in our language). (b) Well formed and good. (c) I took out too many brackets here. Let’s say the formula is ( x ( x c )) ( x = y ), then this is well formed by not good. (d) Well formed but not good. (M3) (1 point) Mark the free and bound variables in the following formulas. (a) x bound2 y bound1 (( y bound1 z free ) ( x bound2 z free ) →∼ ( z free = w free )) (b) z bound1 ( x free = y free ) (c) x bound3 y bound2 ((( x bound3 = y bound2 ) ( y bound2 = z free )) ∧ ∃ x bound1 ( x bound1 y bound2 )) (M4) (a) propositional function (b) propositional function (c) not propositional function (M5) x y (( x y )

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303a5solns - ASSIGNMENT 5 SOLUTIONS MATH 303 FALL 2011 If...

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