hw15 - 41. a. Show that Z / 2 = { [0] , [1] } . b. Let X 1...

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Intro to Abstract Math Homework 15 Fall 2009 Due October 12 Exercise 42. Let S ⊆ P ( A ) be a partition of A . Let = { ( x,y ) | ( X S )( x,y X ) } ⊆ A 2 . Show that is an equivalence relation on A . Exercise 43. Recall the equivalence relation 2 = { ( a,b ) | 2 divides a - b } on Z of Exercise
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Unformatted text preview: 41. a. Show that Z / 2 = { [0] , [1] } . b. Let X 1 = { n Z | n is odd } and X 2 = { n Z | n is even } . Show that the partition { X 1 ,X 2 } of Z is the same as the set Z / 2 ....
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