e310k - MAD 2104 May 20, 2010 Quiz 3 and Key Prof. S....

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Unformatted text preview: MAD 2104 May 20, 2010 Quiz 3 and Key Prof. S. Hudson 1) [30pts] Answer each part with “True” or “False”. You do not have to justify your answers. The sum of an irrational number and a rational number is an irrational number. The product of 2 irrational numbers is an irrational number. An 8x8 chessboard missing the NE and SW corners can be tiled with dominoes. ∅ ⊂ { } ∅ ∈ ∅ The set Q of rational numbers is countable. 2) [20pts] Give an example of f : N → N which is onto but not 1-1. For maximum credit give a formula for f (otherwise, a picture or rule may be OK). Explain briefly why it is not 1-1. 3) [25pt each] Choose TWO proofs, not all three. For maximum credit, use a mix of sentences and formulas arranged into paragraph(s), like most of the proofs given in class. You can continue on the back. a) Prove (0 , 1) is not countable, using Cantor’s argument. b) Prove or disprove: ∀ x,y ∈ R, d x e + d y e = d x + y e c) A ∪ B ⊆ A ∩ B (you don’t have to prove equality).(you don’t have to prove equality)....
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This note was uploaded on 12/27/2011 for the course MAD 2104 taught by Professor Staff during the Fall '08 term at FIU.

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e310k - MAD 2104 May 20, 2010 Quiz 3 and Key Prof. S....

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