222a3s - MATH 222 FALL 2011, Assignment Three (Answer Key)...

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Unformatted text preview: MATH 222 FALL 2011, Assignment Three (Answer Key) 1. Find the number of integers between 1 and 10,000 inclusive which are (a) divisible by at least one of 3, 5, 7, 11; For i = 3 , 5 , 7 , 11, let S i be the set of integers between 1 and 10,000 divisible by i . We need to compute | S 3 S 5 S 7 S 11 | , which is (by the P.I.E.) equal to | S 3 | + | S 5 | + | S 7 | + | S 11 |- | S 3 S 5 | + | S 3 S 7 | | S 3 S 11 | | S 5 S 7 | | S 5 S 11 | | S 7 S 11 | + | S 3 S 5 S 7 | + | S 3 S 5 S 11 | + | S 3 S 7 S 11 | + | S 5 S 7 S 11 |- | S 3 S 5 S 7 S 11 | where | S 3 | = 10 , 000 / 3 , | S 5 | = 10 , 000 / 5 , | S 7 | = 10 , 000 / 7 , | S 11 | = 10 , 000 / 11 , | S 3 S 5 | = 10 , 000 / 15 , | S 3 S 7 | = 10 , 000 / 21 , | S 3 S 11 | = 10 , 000 / 33 , | S 5 S 7 | = 10 , 000 / 35 , | S 5 S 11 | = 10 , 000 / 55 , | S 7 S 11 | = 10 , 000 / 77 , | S 3 S 5 S 7 | = 10 , 000 / 105 , | S 3 S 5 S 11 | = 10 , 000 / 165 , | S 3 S 7 S 11 | = 10 , 000 / 231 , | S 5 S 7 S 11 | = 10 , 000 / 385 , and | S 3 S 5 S 7 S 11 | = 10 , 000 / 1155 ....
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This note was uploaded on 01/15/2012 for the course MATH 222 taught by Professor Huangjing during the Spring '11 term at University of Victoria.

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222a3s - MATH 222 FALL 2011, Assignment Three (Answer Key)...

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