4. Prove that (a + b) ≤a+b≤ a + b for any real numbers a and b. (Hint: Use cases when a, b ≥ 0; a, b < 0; and a & b have different signs.)

Q: 74. Prove that for any real numbers a and b, |b − a|=|a − b|.

A: Given; a and b are any real numbers Consider, L.H.S=b-aWe can write it as,=b+-a=-1-b+a=-1a-b…

Q: Let x be a real number. Which of the following is the same as P(Z x) c) P(Z ≤ -x) d. none of the…

A:

Q: 18.x

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Assume that 2< a < 3 and1<b< 2. Prove that: 2 < a? - 2 < 8. VI

A:

Q: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

A:

Q: Let a,b,c,d be real number with a < b < c < d. Express the set [a,b] U [c,d] as the difference of…

A: We have given that, a, b, c, d are real numbers with a &lt; b &lt; c &lt; d. We need to express a, b…

Q: 2. Find p and q such that 7x+1 5 |5x-1|≤4 implies p ≤: <q

A:

Q: 6. Prove that the statement "If x is a real number such that x² > 4 then x > 2" is false.

A:

Q: Show that if a < c< b, then fave (a, b) = () fave l(a, c) + C - a | favg [c, b]

A: Solution...

Q: Find the maximum value of a, x, +a,x, + .+ax to the condition that x +x, +. + x =1 for given…

A: We need to find the maximum value of a1x1+a2x2+a3x3+...+anxn to the condition that…

Q: Prove that la + b + c| < ]a] + ]b| + |c[

A: Prove that,    a+b+c≤a+b+c

Q: 54. Both of the following statements have the set of positive real numbers as their set of meanings.…

A:

Q: Which x satisfies both Ix - 31 &lt; 2 and Ix - 51 &lt; 1?

A:

Q: Find the set of real values of x for which a) > 3 by/2x- 3/ 0 13 Solve the inequality:x(x² – 6) >…

A: It is given that

Q: A and B are sets of real numbers defined as follows. A-(: |2> 2} B-(: |258} Write AnBand AUB using…

A: Solution:   Given that A &amp; B are sets of real numbers such thatA = z | z&gt;2B = z | z≤8

Q: true or false

A:

Q: 19. Which of the following properties of Real Numbers is NOT true ? * a. Vx ER, x+0 = x b. Vx, y, z…

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Q: Let the domain of x be the set of negative real numbers. Then Vx, (1+ x² > 0) is a true statement a…

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Q: Let S = {-5,-1,0,2/3,5/6,1,sqrt(6),4,5} Determine which elements of S satisfy the inequality.…

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Q: 3. Find all r so that r-1+r-2| < 5.

A:

Q: 2. For all real numbers a, b and c, prove that if a <b <c then a+b+c a < 3 < C.

A: given that a, b, c are real numbers we have to prove that if      a&lt;b&lt;c    then…

Q: Prove that −3 ≤ x ≤ 2 implies that |x² + x − 6| ≤ 6|x − 2|.

A: We have to prove thatWe know that

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: 16. Find the set of real values of x for which:/3 - 2x/S/x + 4/. N.Find the set of values of x for…

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Q: 2. Definition. Let r be a non-negative positive real numbel A square root of r is the Iinique…

A: Note: Square of any real number must be non-negative and addition or subtraction of any two real…

Q: Let R be the set of all real numbers and let a, b eR Ə a> 0 and b > 0. Which of the folbwing is/are…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Prove the inequality √1+x≤1+x2 for x&gt;1.

A: Consider the function. Find its derivative.

Q: Determine real numbers a and b such that |x+a|−b≤0 iff -4≤x≤12.

A: given  x+a-b≤0if -4≤x≤12

Q: What is the set R of all real numbers?

A: Real numbers are the numbers which include both rational and irrational numbers. A real number is a…

Q: If |z| ≤ 2, show that |Im(5 + 2z - 3z³)| ≤ 33.

A: We know, for a complex number z      i) |Im(z)| ≤ |z|      ii) |z̄| = |z| Also, for any two complex…