(1). Prove that adding an irrational number with a rational number is an irrational number, and show whether that is true for multiplication.? (2). Study each of the following in terms of being finite - countable - finite - then find the max, min, upper bound, lower bound, sup and inf for each of the following: . A= (-4, 4), - B= [0,1], C= Q. . D={1,2,...,100}, E- (x: -3 sxs3, XEQ)

Q: - 10 +V-175 al expression 5 er in exact form without decimals. To enter a on

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Q: If a, b. and c are integers such that a|b and c|b. then ac|b.

A: False

Q: If a and b are integers, then a/b is always a rational number. True False

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Q: Determine whether it is possible to express 1 as a liner combination of 1 = m· 44 + n· 91 ,. for…

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Q: 4) Solve the following linear system or indicate the nonexistence of solution. X1 – 2x2 + 5x3 – 3x4…

A: Or, take x2 = k Hence, solution of the system is x1 = 1+2k, x2 = k, x3 = 1, x4 = 2

Q: Which of the following sets are closed? Choose ALL that apply. Show the steps. I. The set of…

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Q: 3. Write the following as symbolic statements. (a) There exists a rational number q such that qr = r…

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Q: The following statement is true. V real number x, 3 an integer n such that n > x. For each value of…

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Q: Let the operations * and e be defined on the set of integers. Find each of the following are…

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Q: Step by step else downvote, with clear handwriting. Prove that for any real number x, there exits a…

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Q: Which irrational number can be multiplied by: 41 to get a product that equals 1 41 O -41

A: We can find the answer as below

Q: Using Fermat’s little theorem to show that 42 | n7 −n, where n is a positive integer.

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Q: Find the distance between K and L on the number line below. ←++ -12 -11 -10 -9 -8 Distance: + -7 -6…

A: Distance between K and L is

Q: 3. If the expression was placed in the form ax where a and b are real numbers, then which of the 2x…

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Q: Need

A: Given that, a can be written as base 10 x= a0+10a1+ ......+10nar We know that, If a divides b…

Q: 2. Use exponent Laws to show whether each expression is true or false. DO NOT CALCULATE to…

A: a. 3632÷3612=36323612                =3632-12    aman=am-n                =363-12                =36…

Q: 1. Prove that the sum of an integer and its square is even

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Q: a. For real numbers a, b, c, and d, find the product. 01 a 0] b. Based on the form of the product of…

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Q: 2a + 56+c —а — 36 — 2с 3a + 76 +c -4a – 96 –c 2. T(а + bx + сх*). |

A: The objective is to write down the matrix of the given linear transformation withrespect to the…

Q: 1. Identify the rule that justifies each step to simpl the expression. 2* (-4') a. = 24 (-4) %3D

A: Since we are given with multiple number of question with multiple subparts and our guideline is…

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Q: Find the total number of integers 'n' such that 2 ≤ n ≤ 2000 and H.C.F. of n and 36 is 1.

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Q: Show that: 15|(24n − 1) for all natural numbers n.

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Q: Find all positive integers n such that 2" – 1 | 3" – 1. - -

A: Given 2n-1|3n-1 ,  for n∈ℤ+ To find if the statement is true.

Q: Let the operations * and e be defined on the set of integers. Find each of the following are…

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Q: If a is a real number and n ≥ 2 is an integer, then which of the following expressions is equivalent…

A: Given expression: an

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A: The given transformation T:ℝ2→ℝ2 First rotates through -7π4radians. then reflects points through…

Q: ) Recall that r > 0 for every positive real number r. Prove that if a and b are positive real…

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