The first section has the following two options: "there exists a positive ε such that," and "for every positive ε" The section select has the following two: "there exists a real number M such that", and "for every real number M" The final selection has the following two: "for every number x greater than M", and "there exists a real number x greater than M such that"   Please complete the correct selection

Q: are there any even numbers greater than 2 which are prime? why or why not?

A: We will find the solution in the following step

Q: Is it possible to raise a positive number b to a power and obtain a negative number? Is it possible…

A: The given statement is " The possibility to raise a positive number b to a power and obtain a…

Q: We need to find all the whole numbers that have remainder 1 upon division by 4 and write our answer…

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Q: Problem 4 [25 points]: Contradiction Given a proof by contradiction of the statement: If n? + 11 is…

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Q: Let f(sub-n) denote the nth Fibonacci number. Show that f(sub-n) is even if and only if n is…

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Q: n² + n+ 8 2 He has just shown you a convincing proof that if the equation is true for any integer k…

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Q: Without using any theorems from the book, prove the following statement: The sum of any two odd…

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Q: We assume that x0. Therefore there exists a natural number n such that n> Since z is fixed we can…

A: Suppose that x and y are 2 distinct real numbers. We have to prove that, there exists a rational…

Q: Is there a real number that is bigger than all integers? If so what is the number and if not what…

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Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: Given any set of 15 integers, must there be two that have the same remainder when divided by 12?…

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Q: 0, the remainder is 2; and when divided by 11, the remainder is 0. remain is 5; when divided by

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Q: Consider the definite integral ∫^3_1 (16 - x2)dx. Let P be the partition of [1, 3] into n equal…

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Q: Show that if n is an odd integer then []

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Q: Please provide justified answer asap:::: Show that n is odd if and only if n^2+4n+1 is even.

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Q: Find an infinite set of your choice whose elements are irrational numbers between 71.8094 and…

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