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MATH135 Lecture Notes - Lecture 2: Natural Number, Prime Number, Open Formula

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azurechimpanzee251

16 Jun 2015

School

University of Waterloo

Department

Course

Professor

Gabrielde Morais Coutinho

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$MATH135 Full Course Notes$

MATH135 Full Course Notes

Document Summary

University of waterloo - fall 2014 - math 135. These objects are called the elements of the set. 1. 2 example. (i) {1, 2, 3, 4, 5, 8} is a set containing six elements. All these elements are numbers. (ii) how many di erent sets can you construct using the symbols { , } , , , 1 and 2 ? (iii) we can de ne a set by specifying a rule its elements must satisfy. What is the set of all positive odd integers smaller than 11? (iv) we can nest sets as elements of other sets. {1, 2,{1, 4}, 5,{1, 2, 3}} is a set whose elements are numbers and sets. (v) answer (ii) again. (vi) you just need to make sure the number of { is equal to the number of } . If s is a set, we use |s| to denote the number of elements of s.

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Related Questions

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ey table is seen below xeecions tor Chapter 1 12, Fori, b â¬ Î.el * b-aa (0 (D 14 ForVEQ r the operation defined in Example 1 on the wr John Sue Henry. P iDFor 15ine if is ass ociative by determining if the final six engu defined ang property (ii)of Theorem 1 . So no element i if the operntion debined in Example 1 of Emle if each element has an inverse Section 1.3 Groups iw comutatityn ild Chapter 3 where the Funda the exercises that follow etermining why they are not Write out the Cayley table for the gru(o)nud lensify thee element the 10 elements of the group Z 18 its operation uses ts in the first coordinnte and +2 in the secotu Ldessity the Zn and write out the Cayley table. Reeall th of each element does Theorem 1.14 tell us aont the entries in the Cayley table ol s xrewp that is set with exactly one element. A {n), will always form group since there 19. What nly one way to define an operation on the set. Be sure to shhow that the properi combination of the usual notice what set the rule is be of a group all hold. 21. We can create even create groupe with games! Consider four cups placed in a ssare patter table. If we have a penny in one of the cups there are four ways we can move it to t cup: Horizontally, Vertically, Diagonally, or Stay nehere it is. We will p, S. To define nn operation, consider two movements in a row, v.e.,m ove the penny as r tells us to, then after that move the penny as y instruets. the set of integers the set of real numbers n the set of positive integers. e set of positive integers. n the set of positive integers. on the set of integers e set of negative integers. we ple, HV D since if we first move it horizontally and then vertically nltogether e moved it diagonally. Create the Cayley table for this group, identify the identity and the inverse of cach element 22. Prove that the set A 0 under matrix multiplication. Is it abelian? 23. Verify that 3(R) is a group using the addition of funetions as defined in Example 13 e set of nonzero rational n he set of nonzero real num n on the set R (-1 Section 1.4 Basic Algebra in Groups 24. Prove the Cancellation Law (Theorem 1.20). Do not use any theorems that occur after it in the text ssociative, commutative, has roof or counterexample fo 25. Assume G is a group and a e G. Consider a fixed integer k and use PMI (Theorem 0.3) to prove that for all nEN, a aYou will need to consider cases here since k can be positive, negative, or o 26. Prove Theorem 1.23 (ii) for the case of n > 0 and m

A student she started this process, how much money will she have after 39 weeks a) Write the multiplication expression that modes this situation b) Evaluate the expression to anpwer the question Write your currently works part time and each week puts 525 Inta her If she had no money saved when savings jar in her.coom, if she had no meney .savins answer the question Write your answer in a complete contextual sentence. 7. If you deposit S If you deposit $950into an account and the accouet balance increases by,1.8% each yea. a) Write the exponential expression that Write the exponential expression that Write the exponential expression that Evaluate the expression to determine the a cent. Write your answer in a complete contextual sentence. t models this situstion if you leave the money in the models this stuation if you leave the money in the account for twe years b) c) c) mode's this situation if you leave the money in the account for five years expression that mode's this situation if you leave the money in the account for twelve years the amount you have at the end of the 12 year period. Round answer to the nearest honey bee colonies ina 8. The number of honey bee colonies has been decreasn g by about 8.5% each year. If there were 25,000 Write the exponential expression that models how many c) Write the exponential expression that models how many honey bees there would be after tern d) Evaluate the expression to determine how many haney bees there particuiar region a) Write the exponential b) the exponential expression that models how many honey bees there would be ater two years ion that models how many honey bees there would be afer tour years e years efter ten years. Since we are dealing with bees, round apprepriately. Write your answer in a complete contextual sentence. 9. A group of friends went out on Friday nignt for dinner ane erinks. The total bill without tax was $173.s0. The tax rate on restaurant food and alconoUs 625%. T he service et the restaura rt was great and they were a bg goup, so they crose to leave a 22% tip. a) Determine the amount of money they left for the tip b) Determine the total amount that they had to pay for their bil, tax, and tip. 10, According to the American Cancer Society in 2015 estimates that 40,290 women will die from dimensional analysis determine your final answer in a complete contextual sentence. Remember to round appropriately 11. According to an a n 2015 it estlmates that 40290 women will die from breast cancer. Using how many women will de per hour in 2015 due to breast cancer. Show al of your work and write article on the Global Issues.org web site."At least 80% of humanity Ewes on less than S10 a day." Source The population of the world ls about 7.3 billion people as of June 2015. Use these two pieces of information to complete the foliowing a) Write the population of the earth in standard form b) Estimate the number of people that live on less than $10 per day. Show all of your work for the estimace. Remember to use numbers that are easy to work with and do not use a calculator Now use a calculator to determine the number of people that live on less than $10 per day, 12. A large elephant can weigh up to 6,350 klograms, which is There is the belief that elephants are afraid of mice as often depicted in cartoons. Compare the weight of the mouse to determine how many times heavier the elephant is than the mouse. Show all of your work and answer in a complete contextual sentence. 6,350,000 grams. An adult mouse can weigh up to about 40 grams weight of the elephant to the write your

Show transcribed image text A student she started this process, how much money will she have after 39 weeks a) Write the multiplication expression that modes this situation b) Evaluate the expression to anpwer the question Write your currently works part time and each week puts 525 Inta her If she had no money saved when savings jar in her.coom, if she had no meney .savins answer the question Write your answer in a complete contextual sentence. 7. If you deposit S If you deposit $950into an account and the accouet balance increases by,1.8% each yea. a) Write the exponential expression that Write the exponential expression that Write the exponential expression that Evaluate the expression to determine the a cent. Write your answer in a complete contextual sentence. t models this situstion if you leave the money in the models this stuation if you leave the money in the account for twe years b) c) c) mode's this situation if you leave the money in the account for five years expression that mode's this situation if you leave the money in the account for twelve years the amount you have at the end of the 12 year period. Round answer to the nearest honey bee colonies ina 8. The number of honey bee colonies has been decreasn g by about 8.5% each year. If there were 25,000 Write the exponential expression that models how many c) Write the exponential expression that models how many honey bees there would be after tern d) Evaluate the expression to determine how many haney bees there particuiar region a) Write the exponential b) the exponential expression that models how many honey bees there would be ater two years ion that models how many honey bees there would be afer tour years e years efter ten years. Since we are dealing with bees, round apprepriately. Write your answer in a complete contextual sentence. 9. A group of friends went out on Friday nignt for dinner ane erinks. The total bill without tax was $173.s0. The tax rate on restaurant food and alconoUs 625%. T he service et the restaura rt was great and they were a bg goup, so they crose to leave a 22% tip. a) Determine the amount of money they left for the tip b) Determine the total amount that they had to pay for their bil, tax, and tip. 10, According to the American Cancer Society in 2015 estimates that 40,290 women will die from dimensional analysis determine your final answer in a complete contextual sentence. Remember to round appropriately 11. According to an a n 2015 it estlmates that 40290 women will die from breast cancer. Using how many women will de per hour in 2015 due to breast cancer. Show al of your work and write article on the Global Issues.org web site."At least 80% of humanity Ewes on less than S10 a day." Source The population of the world ls about 7.3 billion people as of June 2015. Use these two pieces of information to complete the foliowing a) Write the population of the earth in standard form b) Estimate the number of people that live on less than $10 per day. Show all of your work for the estimace. Remember to use numbers that are easy to work with and do not use a calculator Now use a calculator to determine the number of people that live on less than $10 per day, 12. A large elephant can weigh up to 6,350 klograms, which is There is the belief that elephants are afraid of mice as often depicted in cartoons. Compare the weight of the mouse to determine how many times heavier the elephant is than the mouse. Show all of your work and answer in a complete contextual sentence. 6,350,000 grams. An adult mouse can weigh up to about 40 grams weight of the elephant to the write your