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Discrete Structures Homework 2 Due Data:7th April, 2012 1. Given three nite sets X , Y and Z . Show that (a) (X \ Y ) (Y \ X ) = (X Y ) \ (X Y ) (b)...

How can I prove the first & the fifth question of the attached file ?

Discrete Structures Homework 2 Due Data:7th April, 2012 1. Given three finite sets X , Y and Z . Show that (a) ( X \ Y ) ( Y \ X ) = ( X Y ) \ ( X Y ) (b) | X Y Z | = | X | + | Y | + | Z | - | X Y | - | X Z | - | Y Z | + | X Y Z | 2. Let x and y be real numbers. Prove or disprove each of the following (a) d ( x - 3) 2 2 e = d x 2 2 e - 3 x + 5 (b) b ( d x + y e ) c = d x + y e (c) b ( x + y )( x - y ) c = b ( x + y ) cb ( x - y ) c (d) d x - y 2 e = d x 2 e - d y 2 e 3. Let A , B and C be three finite sets. Prove or disprove the following “if A × B = A × C then B = C ”. 4. Let X be a finite set. Prove that a function f : X X is onto if and only if it is one-to-one 5. Let | r | < 1 be a real number. Evaluate X i =0 ir i 1
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