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# 303a6 - ASSIGNMENT 6 MATH 303 FALL 2011 Instructions Do at...

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ASSIGNMENT 6 MATH 303, FALL 2011 Instructions: Do at least 3 points from each section and at least 10 points total . Up to 12 points will be graded, but your maximum score is 10. If you hand in more than 12 points please indicate which ones you want graded, otherwise the first 12 will be graded. Manipulation (M1) (1 point) Let c and c 0 be constant symbols. Show that x ( (( c = x ) ( x = c 0 )) c = c 0 ) is valid using Cohen’s rules (state explicitly which rules you use). (M2) (2 points) Let A ( x ) be a well formed formula with free variable x and let B be a well formed formula with no occurence of x . Let c be a constant symbol and let S = {∀ xA ( x ) , A ( x ) B } Show that you can derive B from S . Use only Cohen’s rules, and state explicitly which rules you use in your derivation. (M3) (1 point) Let E = { a, b, c, d } . Let X = P ( E ) - {{ a, b } , ∅} . What are the maximal elements of X ? What are the minimal elements of X ? Does X have a smallest element? Does X have a largest element?

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303a6 - ASSIGNMENT 6 MATH 303 FALL 2011 Instructions Do at...

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