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Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when it is divided by 6? b. Does there exist a. Is there an integer n such that nhas? such that if n is divided by 5 the remainder is 2 and if? Note: There are integers with this property. Can you think of one?

Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when it is divided by 6? b. Does there exist a. Is there an integer n such that nhas? such that if n is divided by 5 the remainder is 2 and if? Note: There are integers with this property. Can you think of one?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 35E
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is there an integer that has a remainder of 3 when it is divided by 6

EXERCISE SET 2.1 - In each of 1–6, fill in the blanks using a variable or variables to rewrite the given statement. In each of 8–13, fill in the blanks to rewrite the given statement. 1. Is there a real number whose square is –1 ? a. Is there a real number I such that ? 8. For all objects J,if J is a square then J has four sides. b. Does there exist _ such that x =-1? 2. Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when it is divided by 6? a. Is there an integer n such that n has _? b. Does there exist such that if n is divided by 5 the remainder is 2 and if _? Note: There are integers with this property. Can you think of one? a. All squares b. Every square c. If an object is a square, then it _ d. If J _ then J e. For all squares J. 9. For all equations E, if E is quadratic then E has at most two real solutions. e an a. All quadratic equations b. Every quadratic equation c. If an equation is quadratic, then it – d. If E – then E e. For all quadratic equations E, 10. Every nonzero real number has a reciprocal. a. All nonzero real numbers 3. Given any two real numbers, there is a real number in between. a. Given any two real numbers a ánd b.there is a real number e such that c is . b. For any two such that a<e<b. 4. Give any real number, there is a real number that is greater. a. Given any real number r, there is that s is b. For any b. For all nonzero real numbers r, there is for r. s s such c. For all nonzero real numbers r,there is a real number s such that - such that s>r. 11. Every positive number has a positive square root. 5. The reciprocal of any positive real number is Positive. a. All positive numnbers b. For any positive number e, there is c. For all positive numbers e, there is a positive for e. Given any positive real number r, the reciprocal of b. For any real number r, if r is – then c. If a real number r - then 6. The cube root of any negative real number is negative. Given any negative real number s, the cube root of b. For any real number s, if s is: c. If a real number s then. 7. Rewrite the following statements less formally. without using variables. Determine, as best as you can, whether the statements are true or false. number r such that 12. There is a real number whose product with every number leaves the number unchanged. a. Some b. There is a real number r such that the product of r has the property that its a. c. There is a real number r with the property that for every real number s, then 13. There is a real number whose product with every a. There are real numbers u and v with the property that u+v <u-v. b. There is a real number x such that x² <x. c. For all positive integers n, n² 2n. real number equals zero. a. Some has the property that its b. There is a real number a such that the product of a c. There is a real number a with the property that for every real number b, d. For all real numnbers a and b,la+bIslal+lb1.
Transcribed Image Text:EXERCISE SET 2.1 - In each of 1–6, fill in the blanks using a variable or variables to rewrite the given statement. In each of 8–13, fill in the blanks to rewrite the given statement. 1. Is there a real number whose square is –1 ? a. Is there a real number I such that ? 8. For all objects J,if J is a square then J has four sides. b. Does there exist _ such that x =-1? 2. Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when it is divided by 6? a. Is there an integer n such that n has _? b. Does there exist such that if n is divided by 5 the remainder is 2 and if _? Note: There are integers with this property. Can you think of one? a. All squares b. Every square c. If an object is a square, then it _ d. If J _ then J e. For all squares J. 9. For all equations E, if E is quadratic then E has at most two real solutions. e an a. All quadratic equations b. Every quadratic equation c. If an equation is quadratic, then it – d. If E – then E e. For all quadratic equations E, 10. Every nonzero real number has a reciprocal. a. All nonzero real numbers 3. Given any two real numbers, there is a real number in between. a. Given any two real numbers a ánd b.there is a real number e such that c is . b. For any two such that a<e<b. 4. Give any real number, there is a real number that is greater. a. Given any real number r, there is that s is b. For any b. For all nonzero real numbers r, there is for r. s s such c. For all nonzero real numbers r,there is a real number s such that - such that s>r. 11. Every positive number has a positive square root. 5. The reciprocal of any positive real number is Positive. a. All positive numnbers b. For any positive number e, there is c. For all positive numbers e, there is a positive for e. Given any positive real number r, the reciprocal of b. For any real number r, if r is – then c. If a real number r - then 6. The cube root of any negative real number is negative. Given any negative real number s, the cube root of b. For any real number s, if s is: c. If a real number s then. 7. Rewrite the following statements less formally. without using variables. Determine, as best as you can, whether the statements are true or false. number r such that 12. There is a real number whose product with every number leaves the number unchanged. a. Some b. There is a real number r such that the product of r has the property that its a. c. There is a real number r with the property that for every real number s, then 13. There is a real number whose product with every a. There are real numbers u and v with the property that u+v <u-v. b. There is a real number x such that x² <x. c. For all positive integers n, n² 2n. real number equals zero. a. Some has the property that its b. There is a real number a such that the product of a c. There is a real number a with the property that for every real number b, d. For all real numnbers a and b,la+bIslal+lb1.
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