e311k - MAD 2104 Quiz 3 Prof S Hudson 1[30pts Answer True...

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Unformatted text preview: MAD 2104 Sept 29, 2011 Quiz 3 Prof. S. Hudson 1) [30pts] Answer True or False for each: The set of rational numbers is countable. If f : { 1 , 2 , 3 } → { a,b,c } is onto, it is also one-to-one. If A ⊆ Z , then A ∼ N (same card’y). Every 1-1 correspondence f has an inverse function. If f : A → B is 1-1, then f ( A ) = B and f- 1 ( B ) = A . 2) [40pts] 2a) Let g ( x ) = b x c . Find g- 1 ( { } ). 2b) Let A i = ( i, ∞ ) ⊂ R . Find T ∞ i =1 A i and S ∞ i =1 A i . 3) [30pt] Choose ONE proof. Use sentences (rather than Venn diagrams, etc). a) Prove that (0 , 1) is not countable, using Cantor’s Diagonal Argument. b) Prove the absorption law, that A ∩ ( A ∪ B ) = A . Remarks and Answers: The average grade among the top 20 was about 75 / 100, which is pretty good. On the whole, the proofs about sets in 3b were not very good. If you want help with these, please see me or our LA; we might even be able to create a special group session on this. The other problems were mostly good. Unofficial scale:session on this....
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e311k - MAD 2104 Quiz 3 Prof S Hudson 1[30pts Answer True...

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