Need help with this Foundations of Mathematics homework problem. Let A = {a,b} and B = {{a}, {b}, {a,b}}. Which of the following are true?OA CBОА Е ВOAN BAO A U B = В

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Answered: Let A = {a,b} and B = {{a}, {b},…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 12E: Prove that if , , and , then .

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Prove that if , , and , then .
11. (See Exercise 10.) According to Definition 5.29, is defined in by if and only if . Show that if and only if . 10. An ordered field is an ordered integral domain that is also a field. In the quotient field of an ordered integral domain define by . Prove that is a set of positive elements for and hence, that is an ordered field. Definition 5.29 Greater than Let be an ordered integral domain with as the set of positive elements. The relation greater than, denoted by is defined on elements and of by if and only if . The symbol is read “greater than.” Similarly, is read “less than.” We define if and only if. As direct consequences of the definition, we have if and only if and if and only if . The three properties of in definition 5.28 translate at once into the following properties of in . If and then . If and then . For each one and only one of the following statements is true: . The other basic properties of are stated in the next theorem. We prove the first two and leave the proofs of the others as exercises.
Sometimes symbols and abbreviations are used in place of a word or phrase. What word or phrase is represented or abbreviated by each of the following? a)post.b)c)d)e)pt.
Although Pythagoras preceded William Shakespeare by 2,000 years, the philosophy of the Pythagoreans is mentioned in Shakespears The Merchant of Venice. Here is a quote from that play: Thou almost makst me waver in my faith, To hold opinion will Pythagoras, That souls of animals infuse themselves Into the trunks of men. Research the Pythagoreans. What were the main beliefs held by their society? What part of the philosophy of the Pythagoreans was Shakespeare referring to specifically with this quote? What present-day religions share a similar belief? Write a paragraph or two about your findings.

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Let A = {a,b} and B = {{a}, {b}, {a,b}}. Which of the following are true? OA CB ОА Е В OAN BA OAUB B =