Week 14.pdf

# Week 14.pdf - MAT 243 Week 14/15 Written Homework 1 At the...

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MAT 243 Week 14/15 Written Homework 1. At the pet owner’s meeting, there are 20 people who own dogs, and 35 people who own cats. Not everyone owns a cat or a dog, and some people may own both. Justify your answers to the following questions precisely, by using inequal- ities and the inclusion-exclusion principle. Use C for the set of cat owners and D for the set of dog owners. (a) What is the largest number of people who could own a dog and acat, based on the given information? 20. Thus the largest number of people who could own a dog or a cat is 20. This happens when all dog owners own cat(s), that is when D C . (b) Suppose there are a total of 41 people at the meeting. What number of people who own both dog(s) and cat(s) is guaranteed? Since not everyone owns a cat or a dog, there is at least one person in the meeting who neither owns a dog nor a cat, but possibly owns another pet. Thus, if there are 41 people in the meeting, then

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• Spring '14
• RochusBoerner
• Trigraph, Neutering, Theobromine poisoning, ASU School of Mathematical and Statistical Sciences

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