Summer.2012.e1_solutions.pdf

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Department
Computer Science
Course
CSC165H1
Professor
Nathalie Fournier
Semester
Fall

Description
CSC165H1Y Homework Exercise # 1 | Sample Solutions Summer 2012 Worth: 3% Due: By 3:00 PM noon on Tuesday May 29. 1. We will use the following convention: ▯ C is the set of Chloe’s cats. ▯ P(x) means x has spots. ▯ T(x) means x has stripes. ▯ B(x) means x has blue eyes. ▯ G(x) means x has green eyes. (a) Every cat with stripes has blue eyes. i. 8x 2 C;T(x) ) B(x) ii. To ensure that the statement is true, you need to see all Chloe’s cats. If you miss even one cat, you cannot be sure that it does not violate the property. Even a single cat you don’t see could have stripes but not blue eyes. iii. To ensure the statement is false, you only need one cat. It should have stripes, but not blue eyes. (b) Some cat with stripes has no spots. i. 9x 2 C;T(x) ^ :P(x) ii. You need to see one cat, striped but without spots. iii. To ensure the statement is false, you only need one cat. It should have stripes, but not blue eyes. iv. To ensure it’s false, you need to see all cats, to make sure that each either does not have stripes, or has spots. (c) Any cat with neither stripes nor spots has green eyes. i. 8x;(:T(x) ^ :P(x)) ) G(x) ii. You need to see all cats, to make sure that everyone either has stripes, or spots, or green eyes. iii. You need to see one cat, which has no stripes, no spots, and whose eyes are not green. 2. Here is one of two possible ways to ▯ll in the table: Name Eyes Stripes (Y/N) Spots (Y/N) Rosa N Y F
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