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Detem1ine which of the following are equivalent to
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Basic College Mathematics
- In Exercises 7 10, state the property or definition that justifies the conclusion the then clause. Given that s1 and s2 are supplementary, then m1+m2=180.arrow_forwardIn Exercises 1 to 6, which property justifies the conclusion of the statement? If 3x2=13, then 3x=15.arrow_forwardIn Exercises 7 10, state the property or definition that justifies the conclusion the then clause. Given that m3+m4=180, then s3 and 4 are supplementary.arrow_forward
- Let and . Prove or disprove that .arrow_forwardLet (a,b)=1 and (a,c)=1. Prove or disprove that (ac,b)=1.arrow_forward11. (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.arrow_forward
- In Exercises 25 to 32, name the type of reasoning if any used. While judging a science fair project, Mr. Cange finds that each of the first 5 projects is outstanding and concludes that all 10 will be outstanding.arrow_forwardIn Exercises 1 and 2, complete the statement. Exercises 1, 2 If AB=BC, then B is the ?_ of AC.arrow_forwardProve or disprove that AB=AC implies B=C.arrow_forward
- In Exercises 23 to 24, fill in the missing reasons for the algebraic proof. Given: 3(x5)=21 Prove: x=12 PROOF Statements Reasons 1. 3(x5)=21 1. ? 2. 3x15=21 2. ? 3. 3x=36 3. ? 4. x=12 4. ?arrow_forwardIn Exercises 11 to 22, use the Given information to draw a conclusion based on the stated property or definition. Given: 3(2x1)=27; Distributive Propertyarrow_forwardIn Exercises 55 and 56, P is a true statement, while Q and R are false statements. Classify each of the following statements as true or false. a PandQorR b PorQandRarrow_forward
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