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Unformatted text preview: CS 336 Pre-Test 4 Solutions Functions and Induction 5. Functions (continued) 1) * Let D be the set of people. For each of the following relations answer these questions: (i) Is it reflexive? (ii) Is it symmetric? (iii) Is it transitive? (iv) Is it a function? (v) If it is a function, is it one-to-one? (vi) If it is a function, is it onto? a) 2200 x,y ∈ D xCy iff y is a child of x The relation is not reflexive (since I am not my own child), not symmetric (since I am not the child of my child), not transitive (since my child’s child is not my child), and not a function (since I have two children). b) 2200 x,y ∈ D xMy iff y is the mother of x The relation is not reflexive (since I am not my own mother), not symmetric (since I am not the mother of my mother), not transitive (since my mother’s mother is not my mother), but it is a function (since each person has a unique mother). The function is neither one two one (since my two children have the same mother), nor onto (since I am the mother of no one)....
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This note was uploaded on 11/30/2010 for the course CS 336 taught by Professor Myers during the Fall '08 term at University of Texas.
- Fall '08