2 a' b? 6(a +b)? – 12ab >22 2 Prove if a,b >0 then 5. 2 b? ab Inequality of arithmetic and geometric and other's

Q: -. For any integer m and any real number x, if x is not an integer, then [x]+[m - x] = m-1.

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Q: The average of four real numbers is greater than or equal to at least one of the numbers.

A: The average of four real numbers is greater than or equal to at least one of the numbers.

Q: If n is a real number such that n > 2, then n2 > 4. n<2 n² < 4 O Maybe O conclusion is not valid. O…

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Q: A corollary is O a definition that contains a contradiction. O a definition that is provable from a…

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Q: (3) Prove the Generalized Triangle Inequality: if a₁, a2,..., an € R then |a₁ + a₂ + ··· + an| ≤…

A: (3) To prove generalized triangle inequality by principal of mathematical induction. The generalized…

Q: Prove that for all positive integers n, 1 3 2n – 1 1 X...X 4 V3n 2n HINT: You will find it difficult…

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Q: (2) Let x,y and z be real numbers. Show that the distance between a real number x and z is the sum…

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Q: how that the given statement is true. (1) - („")-- (?) - rst we can show that n! (1) - 1([ ow we can…

A: Our objective is to prove the given statement.

Q: For all a > 0 and b> 1, the inequalities In (n) ≤n", n < b are true for n sufficiently large (this…

A: The main objective is to write an inequality comparing (ln(n))8 and n. The expression ln n is…

Q: II. Prove the following are valid (theorems) using resolution: (You must negate!) 1) (~Q->~P)--> (…

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Q: Suppose ne N. Then the following equation is true: () - ) -)-) - + (-1 = 0. + 3 How can this…

A: Let's find.

Q: For each of the remaining items, give a complete proof of the specified form. You need not include…

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Q: Let P(n) be the statement: "a" – b" <n a" – 1 (a – b), where n is a positive integer" -

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Q: When writing proofs by contradiction we begin by assuming the opposite of a statement, and then show…

A: Given are some statements   To Find: Statements which are Contradictions.

Q: When writing proofs by contradiction we begin by assuming the opposite of a statement, and then show…

A: Given that A and B be the set of natural numbers , x be a natural numbers, (a) x∈A∧x∈B∧A∩B=ϕ This…

Q: 4.* Let a > -1 be a real number. Prove that (1+x)" > 1+nx holds for any integer n >0 (this is called…

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Q: DISCRETE MATH - Inclusion-exclusion principle, Euler's totient function, permutations How many…

A: (a) Total number divisible by 2 from 1 to 1000 10002=500....(1) similarly total nos divided by 3…

Q: Given: 21 and 22 are vertical angles, m21 = 5(x + 12), and mz2 =145 Select the reason that best…

A: Given:  Statement 4 is m∠1 =5x+60

Q: -5 10 Select the values that make the inequality g > 2 true. (Numbers written in order from least to…

A: 2.001 2.01 2.1 3 5 7 10

Q: Given: Point B is the midpoint of segment AC, and Select the reason that best supports Statement 6…

A: Point B is the midpoint of segment AC, and segment AC=12 We have to prove: Segment AB=6 And we have…

Q: Given: ZA and ZB are complementary and mZB = 35° Select the reason that best supports Statement 1 in…

A: As it is given that ∠A and ∠B are complementary, the reason for the first statement is given.

Q: Apply the Axioms Test whether you understand each of Euclid's axíoms by matching each of these…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 4. Which of the following properties completes the proof? Given: x - 6 = 4. Prove: x = 10 X-6=4…

A: We have to define which property is used

Q: State and provié the Second isom theom

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Q: Exercise 1. For 2 < x, it is true that 1 1 1 + x4 (1.1) Let's work through the proof to see why…

A: It is given that x≥2, i.e. x≥0 and  we have to prove that, 1x≤1x·1+1x4 therefore taking inverse on…

Q: Let a, m be real numbers. Applying Triangle inequality to u = (m, 0,1,2) and v = (a, -1,-1,0), we…

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Q: 5.68. What is the fundamental inequality of arithmetic and geometric means of n numbers Under what…

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Q: Which of the following sets are infinite? Check all the correct answers! a. the set of natural…

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Q: Buniakovski26 inequality) If neN and a,a2, ... ,an, b,b2,..,bn are real numbers, prove that k%3D1…

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Q: Suppose that m and n are real numbers with m + 5n = 10. Find the least possible value of the…

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Q: Theorem 3. Let p E Z with p > 1. Suppose every integer n, with 2 < n < VP, does not divide p. Then p…

A: i have used the basic ideas of divisor of integer to prove a statement

Q: Tchebychev Inequality a) inequality for k= 1.5, 2.5, 3.5 b) how many stddevs for 50%? 90%?, 98%?

A: As per guidelines we will only answer first three subparts, please repost other subparts for more…

Q: Thàngle Inequality Theorem State if the three numbers can be the meașures of the sides of a…

A: As you have posted multiple questions so according to out guidelines we are solving first question .…

Q: A positive integer is 4 less than another. If 3 times the reciprocal of the smaller integer is…

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Q: When writing proofs by contradiction we begin by assuming the opposite of a statement, and then show…

A: Solution

Q: Give a sufficient but not necessary condition on x for |x|, the absolute value of x, to be greater…

A: Given: x is a absolute value of x. To find: Sufficient but not necessary conditions on x, such that…

Q: 5. Suppose that we roll a standard fair die 100 times. Let X be the sum of the numbers that appear…

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Q: Find all natural numbers n that satisfy two of the given statements 1) Number n is a perfect square.…

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Q: TRUE / FALSE 1. The intersection of two infinite sets is also infinite. 2. If A * B then ANB = Ø. 3.…

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Q: et n > 3 and 2 <k< n – 1. Prove the inequality k + + 2 2. n two ways: (a) algebraic proof, and (b)…

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Q: 5. Give a good statement of the converse of the Pythagorean theorem. In a couple of sentences…

A: We have to  write a good statment of converse of Pythagoras theorem.

Q: which Square of Pesitive. not possible number es always as a Jdene, there is Such exisf no

A: It depends on which function we have under the given domain conditions. If there is no function…

Q: If the binding of the book is broken, then the student will have to pay for a new one. Lisa has to…

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Q: 5. (10 points) Prove that for all positive real numbers r and y, one has the inequality > 2 (u+ 112…

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Q: A 4. Which statement could be proved false using a counterexample? All acute angles are less than 90…

A: The angle which is less than 90 degree is called acute angle

Q: 2. Show between any two irrational numbers there is an irrational number. (Hint: Assume r and s are…

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Q: Use the arithmetic mean-geometric mean inequality to prove: (2)(6)(10)...(4n – 2) < 2" · n", n =…

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Q: Prove this inequality: (n+1)! < (n+1)^(n+1)

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Q: 3.The inequality x2 2 4 is true for all counting numbers O 1. True O 2. False

A: No, the given statement "the inequality x^2 ≥ 4 is true for all counting numbers. " is not true.…