# 303a2 - conditions does S P E = P S E(P3(3 points(a Give an...

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ASSIGNMENT 2 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 E = { a,b,d,q } . Let A = { a } and let B = { b,d } . What is ( A 0 B ) 0 ? (M2) (1 point) Let A = { 1 , { 3 , 8 } , 4 } and B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 } . What is A - B ? (M3) (1 point) Is {{{∅} , {{∅}}} , {{{∅}}}} an ordered pair? If so, what are the ﬁrst and second coordinates? (M4) (1 point) Is {{{ a,b } ,b }} an ordered pair? If so, what are the ﬁrst and second coordinates? (M5) (2 points) Let A = { a } and B = { a,b } . Explicitly list the elements of P ( P ( A B )) and circle those which are in A × B . Pure Math (P1) (3 points) The 6 exercises on complementation from Halmos p18 (P2) (4 points) ( this is in Halmos on p21 ) For any set E , what is S P ( E )? Under what
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Unformatted text preview: conditions does S P ( E ) = P ( S E )? (P3) (3 points) (a) Give an example to show that A × B 6 = B × A in general. (b) Under what conditions does A × B = B × A ? Ideas (I1) (4 points) Give a diﬀerent deﬁnition of ordered pair (other than just swapping the coordinates). Explain why your deﬁnition still works, and describe what is better or worse about it compared to the usual deﬁnition. (I2) (2 points) Look up (or remember) the sieve of Eratosthenes. Write down what it is using the notation T C for some C . (I3) (3 points) Compare De Morgan’s laws for sets with De Morgan’s laws in logic (look them up if you don’t know them). Find where we implicitly used the logic version in the proof of De Morgan’s laws for sets. 1...
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## This note was uploaded on 01/30/2012 for the course MATH 310 303 taught by Professor Rwk during the Spring '11 term at Simon Fraser.

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