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(a) Someone has claimed that since 14 is itself a multiple of 7, then there are more multiples of 7 than there are of 14. Show this is false by establishing 7Z - 14Z. (Do this formally, by establishing the appropriate function.)

(a) Someone has claimed that since 14 is itself a multiple of 7, then there are more multiples of 7 than there are of 14. Show this is false by establishing 7Z - 14Z. (Do this formally, by establishing the appropriate function.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q3 (Recall the notation: For any set S CR and any k e R, kS = {ks : s E S}.) (a) Someone has claimed that since 14 is itself a multiple of 7, then there are more multiples of 7 than there are of 14. Show this is false by establishing 7Z - 14Z. (Do this formally, by establishing the appropriate function.) (b) This person went on further to claim that there are more integers that are not divisible by 7 than are divisible by 7. (So, they are claiming that the cardinality of the set of integers not divisible by 7 is larger than the cardinality of the integers divisible by 7.) Is this claim true? (Justify your answer, but the justification can be informal.)
Transcribed Image Text:Q3 (Recall the notation: For any set S CR and any k e R, kS = {ks : s E S}.) (a) Someone has claimed that since 14 is itself a multiple of 7, then there are more multiples of 7 than there are of 14. Show this is false by establishing 7Z - 14Z. (Do this formally, by establishing the appropriate function.) (b) This person went on further to claim that there are more integers that are not divisible by 7 than are divisible by 7. (So, they are claiming that the cardinality of the set of integers not divisible by 7 is larger than the cardinality of the integers divisible by 7.) Is this claim true? (Justify your answer, but the justification can be informal.)
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