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Unformatted text preview: Sample final This is the subset of the union of two actual finals I have given in the past. I have deleted many questions that we did not cover the material on. You should make sure you can solve easy problems! you can practice by trying the problems in the book. 1. Name 2. Give an example of a tautology. 3. Define f ( x ) so that { x  f ( x ) } = { 1 } . 4. Define two sets A and B such that A B . 5. Define two sets A and B such that A B . 6. Define two sets A and B such that A B = A . 7. Define two sets A and B such that  A B  = 4. 8. Define a set A whose power set only has one element. 9. Define, using set builder notation (e.g. { x  blah } , the set of all odd integers. 10. Define a function on the set { 1 , 2 , 3 } that is onetoone but not onto or indicate that this can not be done. 11. Define a function on the positive integers that is onto but not onetoone. 12. Define a relation on the positive integers that is an equivalence relation....
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This note was uploaded on 03/07/2010 for the course MA 2312 taught by Professor Johniacono during the Spring '10 term at NYU Poly.
 Spring '10
 JohnIacono
 Math

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