303a4solns - ASSIGNMENT 4 SOLUTIONS MATH 303, FALL 2011 If...

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Unformatted text preview: ASSIGNMENT 4 SOLUTIONS MATH 303, FALL 2011 If you find any errors please let me know. Manipulation (M1) No the integers with the usual are not well ordered. We can see this because the set of all integers has no least element, since for any n Z , n- 1 Z and n- 1 < n . So it is certainly not the case that all subsets of the set of all integers have a least element, and hence this is not a well order. (M2) A B = { (1 , 4) , (1 , 5) , (2 , 4) , (2 , 5) , (3 , 4) , (3 , 5) } , which has size 6. Notice that 6 = #( A )#( B ) . (M3) B A = {{ (8 , 6) , (96 , 6) } , { (8 , 6) , (96 , 7) } , { (8 , 6) , (96 , 8) } , { (8 , 7) , (96 , 6) } , { (8 , 7) , (96 , 7) } , { (8 , 7) , (96 , 8) } , { (8 , 8) , (96 , 6) } , { (8 , 8) , (96 , 7) } , { (8 , 8) , (96 , 8) }} which has size 9. Notice that 9 = (#( B )) #( A ) . (M4) P ( A ) = { , { 5 } , { 7 } , { 83 } , { 251 } { 5 , 7 } , { 5 , 83 } , { 5 , 251 } , { 7 , 83 } , { 7 , 251 } , { 83 , 251 } , { 5 , 7 , 83 } , { 5 , 7 , 251 } ,...
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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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303a4solns - ASSIGNMENT 4 SOLUTIONS MATH 303, FALL 2011 If...

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