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HW2_199

# HW2_199 - HOMEWORK 2 DUE Fri Oct 7 NAME DIRECTIONS Turn in...

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HOMEWORK 2 DUE: Fri., Oct. 7 NAME: DIRECTIONS: Turn in your homework as SINGLE-SIDED typed or handwritten pages. STAPLE your homework together. Do not use paper clips, folds, etc. STAPLE this page to the front of your homework. Be sure to write your name on your homework. Show all work, clearly and in order . You will lose point 0.5 points for each instruction not followed. Questions Points Score 1 1 2 1 3 1 4 2 5 3 6 1 7 1 Total 10 1

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HOMEWORK 2 DUE: Fri., Oct. 7 NAME: Problem 1: (1 point) Suppose A negationslash = and B negationslash = . Show that A × B = B × A iff A = B . Problem 2: (1 point) If A , B , and C are finite sets, show that # ( A B C ) = # A + # B + # C # ( A B ) # ( A C ) # ( B C ) + # ( A B C ) . Problem 3: (1 point) If a , b Z , show ( a )( b ) = ab . Problem 4: (2 points) If a , b Z , (a) (1 point) Suppose 0 <a and 0 <b . Show that a<b iff a 2 <b 2 . (b) (1 point) Suppose a< 0 and b< 0. Show that a<b iff b 2 <a 2 . Problem 5: (3 points) If n , k are non-negative integers, we define the binomial coefficient, ( n k ) , by parenleftbigg n k parenrightbigg = n ! k !( n k )! , where n ! = n · ( n 1) · · · 2 · 1, and we set 0! = 1. (a) (2 points) Prove that parenleftbigg n r parenrightbigg + parenleftbigg
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HW2_199 - HOMEWORK 2 DUE Fri Oct 7 NAME DIRECTIONS Turn in...

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