If x is any real number, then

Q: Let n be a real number and let e be a positive real number. Determine whether there exists a real…

A: see the attachments

Q: Find the cardinal number of the set of all solutions to x2 =100

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Q: Show by contraposition that for positive real numbers a and b, if ab - a - b ≥0 then a and b are…

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Q: Prove that if x is a real number, then ⌊2x⌋ = ⌊x⌋ + ⌊x + 1/2 ⌋.

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Q: If a and b are any real numbers, is the statement a * b = b * aalways true? Why or why not?

A: Given that, a and b are any real numbers.   The objective is to decide whether the statement a×b=b×a…

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

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Q: If a = 2a - a² and b =1-(1-a), show that a = b for all natural numbers n. Assume that a, is a fixed…

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Q: If 60 % of x is 420 then find x

A: Given ,  60% of x is 420  i.e  60% × x = 420  We have to find x

Q: List the members of each sets. 1( x/x is a real numbers such as x^3= 27) = 2. (x/x is an integer…

A: We will find each elements of the set

Q: If 40% of x is 300 then find x

A: Given,40% of x is 300then, x = ?

Q: Given any two distinct real numbers, there is a real number in between them.a. Given any two…

A: It is given that any two distinct numbers there is a real number between them.(a)The two distinct…

Q: Let æ be a real number. Show that [3r] = [a] + æ + + 3

A: Here we have to show that 3x=x+x+13+x+23

Q: Prove or disprove if x2-1 is odd, then x is even

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Q: Let x be a real number. For what value of x, the statement if x2 < 0, then a <0 is FALSE? O x=-1.5 O…

A: From given statement

Q: Let x be a real number. Prove that x is an integer if and only if [0.891a] + [0.109æ] =

A: Solution: Definitions floor function: It takes real number x as an input and gives as output the…

Q: Prove that for every real numbers a, b, and c, where b a is not equal to zero, if a +b = c, then=+1

A: Given,            For every real numbers a,b and c, where b is not equal to zero.            if…

Q: Name the subset(s) of the real numbers to which each number belongs. 1. 2/3 2. -1

A: The real numbers have the following important subsets:       Rational numbers, irrational numbers,…

Q: Show by contraposition that for any real number x if -5 <x<4 then x2+x- 20 <0

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Q: Determine whether the following statement is true or false: T $ {x|x is an irrational number}.

A: π∉x x is an irrational number.

Q: Prove that if æ is a real number, then [2a] = [x] +

A: If x is a real number then  to prove- 2x=x+x+12 Greatest integer function is denoted by [x] for any…

Q: . Use the definition of e" to show that for any real numbers 0, 01, and 02. a. ee, = 0, +0,). b. e"…

A: We have to prove that  a.  eiθ1·eiθ2=eiθ1+θ2b.  e-iθ=1eiθ We know the definition from Euler's…

Q: If a + 0, the degree of ax" is

A: The degree of a polynomial is given by the highest exponent appearing on the variable term. For…

Q: 10. Let x be a real number. Prove that at least one of the numbers /2 – x or /2 +x is irrational.

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Q: If 75% of x is 1500 then x is

A: Given ,  75% of x is 1500 then  We have to find x  We know that ,  75% of x is 1500 means

Q: Use proof by contradiction to show that there is no positive real number x such that (x-2)/x ≥…

A: In an inequality, if a positive number is multiplied then there is no change of sign of inequality.…

Q: For every pair of integers x and y, if x – y is odd, then x is odd or y is odd.

A: Let x-is even integer and y-is even integer. x=2m, y=2n

Q: For any real numbers a and b: If a -b

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Q: Let x and y be real numbers. Disprove: If |x| < |y| then |x+1|< |y+1]. Let x, y, and z be real…

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Q: If x is even and y is odd, show that (x + y)? is odd.

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

A: Given that m is an integer and x is a real number which is not an integer. we know that for any real…

Q: In interval notation, [2, 5) represents the set of real numbers between______ and_______ ,…

A: The given statement is, In interval notation, [2, 5) represents the set of real numbers…

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

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Q: There exists a real number R which is greater than 5 O R= {7, 42,2t, and 97/3) O R= {1, 2, and T/6}

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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: {x|x is a natural number and 20<x<24}

A: x | x is a natural number and 20&lt;x&lt;24

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 a<b<c<d, then prove that for any real 2,

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Q: { O if k is a multiple of 2 r if k is not a multiple of 2 W where r can be any real number

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Q: Let x be a real number. Prove by contrapositive that if x + 5x = 40, then x < 3.

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Q: Let a, b, and c be nonzero real numbers. Show, without direct evaluation, that 1 1 1 1 0. a bc ac ab

A: To show the given condition

Q: Let a and b be real numbers. Prove that, if a + b >= 100, then a>39 or b>60

A: Let a and b be two real numbers, a, b∈ℝ.

Q: Prove that if a, 6, and c are positive real numbers with ab = c, then a < yc or 6 < Vc.

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Q: Use the definition of e to show that for any real numbers 0, 01, and 02, a. "": = M0, +0,) b. e" =…

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Q: Let x, Y be positive real numbers. If x2 – y² =1, then x or y (or both) is not an integer.

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Q: Let x be a real number. Prove by contrapositive that if x' + 7x = 90, then x < 4.

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Q: Let a and b be real numbers. If a x b=0, then a = 0 or b = 0. %3D O True O False

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Q: Which of the following are not real numbers? (Select all that apply.) (−6)1/2 (−6)1/3 (−6)1/4…

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Q: Let z and y be real numbers. Prove that, if 5æ + y > 11, then z> 2 or y > 1.

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