CS 336 PreTest_sets_3 - CS336PreTest3 RelationsandFunctions...

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CS 336 Pre-Test 3  Relations and Functions 4. Relations  1) * For each of the following sets, state whether or not it is a partition of {0, 1, 2, 3, 4, 5, 6, 7,  8, 9, 10}. a) {{0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, {10}} b) { , {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, {10}} c) {{1, 2}, {3, 4}, {5, 6}, {7, 8}, {9, 10}}  d) {{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 7}, {7, 8}, {8, 9}, {9, 10}} 2) * For each of the following relations, state which of these properties hold: reflexivity, symmetry, transitivity, and antisymmetry. a) “equality” defined on strings b) “inequality” defined on strings
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c) “less than” defined on  N  (the natural numbers) d)  “subset of” defined on the power set of  N 3) Let  A  be a set of people.  Let  F  be the friendship relation on  A .  In other words,  xFy  iff  x  is  friends with 
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CS 336 PreTest_sets_3 - CS336PreTest3 RelationsandFunctions...

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