Suppose E = { € R : x² + x < 6}. Select the best answer. The set E is empty. The supremum of E is an irrational number. The set E is not bounded above. The supremum of E is a rational number but not an integer. The supremum of E is a natural number.

Q: If A = {x+|x-1| : xER), then which of ONE the following statements is TRUE? A. Set A has a supremum…

A: We use the definition of modulus function to solve this problem.

Q: Find two irrational numbers a and b such that a is rational.

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Q: Prove with contrapositive proof.

A: The contrapositive of the statement  is If the statement  is true then it's contrapositive Is also…

Q: If A = {x+|x-1| : xER), then which of ONE the following statements is TRUE?

A:

Q: If æ is an irrational number, then it is the case that sup{q E Q : q< x} < x.

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Q: 20. Prove: Let x and y be real numbers. If x is rational and y is irrational, then x + y is…

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Q: (c) Let us assume the facts from part (b) for all a, b e R, i.e. as < bs whenever a < b. Let SCR be…

A: Given that S~=x∈ℝ|x3∈S And S⊂ℝ is bounded above. We say that S⊂ℝ is bounded above if  and if…

Q: Prove the statement if it is true, and give a counterexample if it is not true. a. For every real…

A: Both the subparts are solved with explanation.

Q: Let a,b and x be real numbers with a0. Show that there exists a rational number t such that a <

A: We know that the real numbers are densely ordered. This means that between any two distinct real…

Q: Let x, y ER. Ifx<y with x and y very close to each other. Then which of the following statements is…

A: Given x &lt; y

Q: If x ER is irrational and r E Q, show that r + x ER is irrational.

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Q: Typewritten for an upvote

A: Let, x is any real number and A is subset of R.

Q: If x and y are real numbers and x>1, prove that there exists a positive integer n such that xn > y

A:

Q: Incorrectly, we usually say that when we multiply any number by ten we “add” a zero to the number.…

A: a) Jushua is wrong because the correct answer is 10×1.3=13 b) If a whole number is multiplied by 10…

Q: Suppose E = { € R: x² + x ≤ 1}. Select the best answer. The supremum of E is a rational number but…

A: The given set E=x∈ℝ: x2+x≤1. We have to find the supremum of the set.

Q: If r and s are real numbers and r < s, then there exists a positive integer t such that r+t = s.…

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Q: A is a subset of the real numbers, R.

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Q: If a and b are both rational numbers such that a = 0 and b = 0, then is also a rational number.

A: we say a number is rational when it is in p/q form where p≠0.

Q: Find the value of x to make a counterexample to the conjecture. Conjecture: For all numbers x,…

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Q: Let 13 20 x 20+ y = 2 be the equation of a curve in the xy-plane. Find the equation y = T(x) of the…

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Q: T or F True or not: Every nonempty set of rational numbers that is bounded has a largest number.

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Q: (i) Show that √6 + √7 is an algebraic number.

A: We are answering only the first question as per the guidelines. Please repost the other question to…

Q: If S is a nonempty subset of the negative rational numbers, then: 3x e S(Vy e S(x > y)). O true O…

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Q: Give an example of numbers a and b such that |a + b| &lt; |a|+|b|.

A: To give an example of numbers a and b such that

Q: For each of the statement below, decide whether it is true or false, and prove your claim. (a) For…

A: Sum , difference, product and division of rational numbers is rational

Q: If S is a nonempty subset of the negative rational numbers, then: Jx e S(Vy E S(x > y)). true O…

A: Note: Rational numbers are countably infinite. So there is no largest rational number and no…

Q: C and D are sets of real numbers defined as follows. C= {z | z>3} D={z | z≤9} Write CUD and Cn D…

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Q: a. Show that for any real number x, if x> 1 then | x4 |≤| 23x4 + 8x² + 4x |.

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

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Q: If x and y are positive rational numbers, prove that there exists a positive integer n such that nx…

A: Given: If x and y are positive rational numbers, prove that there exists a positive integer n such…

Q: Graph on the number line, and express in interval notation. The set of all real numbers between 1…

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