am_lect_06 - Announcements Second HW released last Friday...

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Announcements Second HW released last Friday, due this Friday http://www.cs.uiuc.edu/class/sp10/cs173
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Recap: How to prove/disprove statements Examples from last time : x Q , x 2 = 2.25 x Q , 2 x Q Today’s example: Show that the square of any odd number is odd k Z odd , k 2 Z odd k Z , k is odd k 2 is odd Prove Disprove Existential statements x , P ( x ) Universal statements x , P ( x ) Show P ( x ) is true for some specific x Show P ( x ) is false for some specific x Show P ( x ) is true with a general argument Show P ( x ) is false with a general argument Unpack/repack definition Proving an implication
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Definitions of even and odd integers Definition : n Z is even if m Z , n = 2 m Definition : n Z is odd if m Z , n = 2 m + 1 Important : In definitions: A if B A B Everywhere else: A if B “if B then A B A Is zero even or odd?
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