Problem Set 1

# Problem Set 1 - University of California San Diego ECE 109...

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University of California, San Diego ECE 109: Problem Set #1 1. An ice cream store manufactures five basic flavors (vanilla, chocolate, mint, strawberry, and fudge) of ice cream, and then creates its specialty flavors by mixing two or more basic flavors in equal proportions. ( a) How many specialty flavors can be obtained by mixing three basic flavors? How many of these contain chocolate? How many of these contain either chocolate or fudge or both? How many of these contain either chocolate or fudge but not both? ( b) How many distinct flavors (including basic and specialty flavors) of ice cream can the store offer? 2. Express each of the following events in terms of the events , and , and the operations of complementation, union, and intersection: (a) at least one of the events occurs; (b) at most one of the events occurs; (c) none of the events occurs; (d) all three events occur; (e) exactly one of the events occurs; (f) events and occur, but not ; (g) either event occurs, or if not then also does not occur.

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