A and B are sets of real numbers defined as follows. A={x|x≥1} B={x|x>7} Write A∪B and A∩B using interval notation

Q: Let a and b be real numbers. Prove that | a b | = | a | | b | , b ≠ 0

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Q: 13. Let U be the set of real numbers, A = {x |x is a solution of x - 1 = 0}, and B ={-1, 4}.…

A: Let's find.

Q: Prove by contradiction that for any positive two real numbers, x and y, if x·y ≥ 100 then either x…

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Q: B and C are sets of real numbers defined as follows. B-x |x<2} c={x |x27) Write Bn Cand BUC using…

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Q: If f(x) = and g(x) = z+3 %3D I-1 H-2 The domain of fogis the set of all real numbers except z+1

A: For f(g(x)) to be defined first g(x) needs to be defined

Q: If f(x, y) = 2√x² + y² - 16, then the domain of f is the set D = {(x, y)]x² + y² ≥ 4}. Select one:…

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Q: Determine k so that; is singular.

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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: If a,b,c,d are in distinct real number in A.P. Such that 2(a-b)+c(b-c) +(c-a) =2(a-d)+(b-d) +(c-d)'…

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Q: 9. Using the notation of the previous problem, prove that for sets A, B, C, DE P(X) AAB = CAD → AAC…

A: First we take forward part and take an element in A∆C and show that it is in B∆D and then take…

Q: Let Q(x, y) be the statement "x + y = x – y." If the domain for both variables consists of all…

A: Given that Q(x, y) be the statement                         x + y = x -y .

Q: Let ā = and b . Find 3ā + b. -

A: We will simply use vector addition rules to find the answer

Q: What is the set of real values of c so that (A) [0, 1] (B) [0, 2] (C) [1, 2]

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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 f'(x) and g'(x) exist and f'(x) > g(x) for all real a, then the graph of y = f(x) and the graph…

A: In this question we have to find how many time functions will intersect to each other.

Q: Prove that the value of an expression (a - 1)(a - 3)(a - 4)(a - 6) + 10 is positive for every a…

A: To prove that   the value of an expression (a - 1)(a - 3)(a - 4)(a - 6) + 10 is positive for every a…

Q: d) The product of two numbers, a and b is zero if and only if at least one of them is zero; e) For…

A: We have to solve d,e,f.

Q: If n is any real number and f(x) = x", then f'(x) = nx"-!

A: Why does ddxxn=nxn-1                 ddxfx=limh→0fx+h-fxh…

Q: F and H are sets of real numbers defined as follows. F={y|y>1} H={y|y<8} Write FU H and F N H using…

A: NOTE: Refresh your page if you can't see any equations. . given inequalities:   use the number line…

Q: Let x and y be postive numbers such that x+2y=50. Fing the values of x and y that make the quantity…

A: Here we will use the concept of maxima and minima to solve this question

Q: Suppose that E and F are points on the number line . If EF = 11 and E lies at 3, where could F be…

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Q: Find a and b such that 2 1 = a -4 + b -4

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Q: Prove that for all real numbers a, b, c, d, the quantities a – b², b – c², c – ď² , d – a² cannot…

A: We will try to prove the given statement by contradiction.   Let us assume that all of a-b2, b-c2,…

Q: Show that if f1(x) isΘ(g1(x)), f2(x) isΘ(g2(x)), and f2(x) ≠ 0 and g2(x) ≠ 0 for all real numbers x…

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Q: Let Q(x, y) be the statement "x + y = x - y." If the domain for both variables consists of all…

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Q: State all integer values of x in the interval 3 -7

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Q: If f(x, y) = 2√/16 - x² - y², then the domain of f is the set D = {(x,y)|x² + y² ≤ 16}. Select one:…

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

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Q: 6.3.6 For each real number x, let Ay = {3, –2} U {y E R : y > x}. Find U Ax and N Ax. xER xER

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Q: Show that if a, b are real numbers then: |a| + |b| > |a + b|

A: If a,b are real numbers, then  PT a+b≥a+b Proof: Let a,b∈ℝ Let a and b denote the absolute value of…

Q: 1 If x is a real number, then is x² + x4 equal to а. V1 + x² b. 1 xV1+ x? c. xV1+x² d. æ|/1+ x² 1 е.…

A: Let's find.

Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              =&gt; k(15 - 13) = 2k for any integer k              =&gt; 15 k -…

Q: Let Q(x, y) be the statement "x + y = x – y." If the domain for both variables consists of all…

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Q: Let a,b be two real numbers and define a*b=ab+a+ b.

A: Given:

Q: |u|> c is true for all real numbers if c _ 0.

A: |u|&gt;c is true for all real numbers if c ____ 0.

Q: x-4 f(x) = In %3D x² – 5x + 6)

A: Given:  f(x)= ln x-4x2-5x+6⇒ f(x) =…

Q: If A= xe Z:2" = 1 and B = {x e Z:-4 < 3x-1<11}, then find n(A×B),where Z is a set of integers.

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Q: B. Find a number that provides a counterexample to show that a given statement is false x, x³…

A: For all number x, (x+1)(x-1) over (x-1) is equals to x+1

Q: Q2) If f(x) = (x), and g(x) = (2- x)i find (gof) (x) and the domain of (gof)(x).

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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: 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: The floor function is defined as bxc = max{m ∈ Z | m ≤ x}. Effectively, the floor function is the…

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Q: Translate 3xvy(xy = y) into English, where the domain for each variable consists of all real…

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Q: If b is a positive real number with b ≠1, then for all positive real numbers x and y we find

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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: If f(x, y) = 2√16- x² - y², then the domain of f is the set D {(x, y) x² + y² ≤ 16}. Select one: O…

A: Given - fx,y=216-x2-y2 To determine whether the set D= x,y|x2+y2≤16 is the domain set of f or not.

Q: Determine all pairs (x, y) of integers that satisfy x* + (x+ 1)4 = y² + (y + 1)²

A: Given equation x4+x+14=y2+y+12Simplify above equation we get that 2x4+4x3+6x2+4x+1=2y2+2y+1now we…

Q: f(x) = x+3x−2x+3x−2 and g(x) = x−1x+1x−1x+1 . The domain of f ∘∘ g is the set of all real numbers…

A: Use fog(x) =f(g(x))

Q: { // - // | m, n {N} write the infimum, mini mum, maximum and supremum of each of the ff. sets…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.