1. Find the supremum, infimum, maximum, and minimum of each subset of R, if it exists. A = U[-2, 1- TEN a. A: sup A max A inf A min A b. B = {":ne N} sup B max B inf B min B c. C = {re Q:r² ≥ 1} sup C max C inf C min C 2

Q: 6. Solve V²+1 = 0 for square region (a x a) here specified at the edges, take h = k = 2. Hint: no…

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Q: For the predicate P(x, y) ::= [x + 2 = y], choose all the pairs of x and y such that P(x, y) is…

A: Given query is to find the correct option for the expression.

Q: 2. Show that for any real number c, there is exactly one integer in the interval (c,c + 1].

A: As per guidelines, I can do only first question.

Q: Evaluate the fraction

A: 1. Given: vu=u+8 To find: v-3t+10 Solution: We have vu=u+8 v-3t+10=-3t+10+8=-3t+10+8=-3t+18…

Q: white the funetion in the form flx)- for the given value of K, and demon c flx)= r 2 flx)= x3-x-14x…

A: Given    q(x) is the quotient when F(x) is divided by x + 1 and r is the remainder.

Q: Prove that (ab + cd)² ≤ (a² + c²)(b² + ď²) for all a, b, c, d ɛ R.

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Q: = Let a, b, and d be positive integers. Prove that if (a, b) : divides a, then (d, b) = 1.

A: Definition of gcd (a, b) =1 is a and b does not have common prime divisor. Using this we can easily…

Q: Select all the real numbers M among the choices below such that the two planes given by r. -2= -3…

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Q: 1. Let X be the set of real numbers with the usual pseudometric. Find the derived set and the…

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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: B and C are sets of real numbers defined as follows. B={y|y≥4} C={y|y<7} Write B n C and B U C using…

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Q: Find the value of a for which V= 8 a 4 is in the set a = 4 -5 0 -8-8-8} 4 -3 H = span

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Q: Challenge #7 Plot five parabolas with the same x-intercepts (black), but different vertices (other…

A: Given:  Points : ( -4 , 0 ) and ( 4 , 0 )   Vertex (h,k ) :  Red : ( 0 , 80) Blue: ( 0 , 48 ) Green:…

Q: 1 1. -to prove that x+y|# | x|+ | y| for all real numbers d) Use x = and y = %3D x and y.

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Q: 11. Solve the following and state the restriction(s) on x : x- 2 a) -3 2x+3 3 >2 2x+4 b) X+3 X+7 c)…

A: To solve the given equations and find restrictions on x

Q: F and H are sets of real numbers defined as follows. F={y|y21} H= {y |y>7} Write FUH and FnHusing…

A: A set is a well-defined collection of objects. The objects, which belong to the set, are called…

Q: H3 H4 45 45 40 H1 H6 30 75 75 20 25 H5 40 H2 45 100 90 45 80 H7 H10 50 15 H8

A: Given: A graph with 10 nodes. To find the minimal distance from H1 to any of the other nodes.

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: Assume that A, B, C and D are sets. Verify that (A x B) U (C x D) ≤ (AUC) x (BUD).

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Q: Suppose that x is a real number and that UCR. Prove that the following two conditions are…

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Q: Find the value of a for which V= 8 a a 4 is in the set H = span 4 4 -5 0 -3

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Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a&lt;b means that a…

Q: Let u = (2, -2, 3), v = (1, -3, 4), and w=(3, 6, -4). Evaluate the following 1. ||3u-5v+w||…

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Q: Show that ACB implies |A|≤|B|.

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Q: Q closed over multiplication? (Y/N) 6. Is N closed over multiplication? (Y/N)

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Q: Show that if AB={0}, then P(A)≤P(B).

A: Given that

Q: Suppose A and B are nonvoid, bounded, disjoint subsets of R. Mark all of the properties that must be…

A: Answer given below.

Q: Find the value of a for which v= 8 a -4 -12 is in the set 4 0 -4 -1 0 {6E9 2 -3 5 -3 -4 2 H = Span

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Q: Let a,b be two different points in R^n one. We notice that d=(a,b)>0 (why is that so ?). Prove that…

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Q: Express each set below using the roster method. Write all elements in increasing order. Do not…

A: Introduction: In Maths, sets are a collection of well-defined objects or elements. A set is…

Q: um value of -+ b + c c + a + a+b

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Q: Select all the real numbers Mamong the choices below such that the two planes given by and r. 2 - M…

A: We can calculate using the given information