Let G = Express b3abab3a in the form biaj.

Q: Find all values of x such that fx>0 and all x such that fx<0

A: f(x)=-1x39-3 To find x values  such that f(x)&gt;0 we find out x intercepts To find x intercepts ,…

Q: Prove: If x, y, z are integers with x2 + y? = z², then either x or y (or both) is even. Hint: Do a…

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Q: 4|\B Prove that (V3+ i)6 = -64

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Q: Use proof by contradiction approach to prove that VxM) V N(X)

A: This is a problem of Predicate Logic.

Q: How to prove that a formula A is valid iff ¬A is unsatisfiable?

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Q: Let A = [0, 1] – Q. Determine if A is countable or uncountable. Prove your claim.

A: Let

Q: Let G = &lt;a, b | a2 = b2 = (ab)2&gt;a. Express b2abab3 in the form biaj.b. Express b3abab3a in the…

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Q: Show that gcd(a, bc) = 1 if and only if gcd(a, b) = 1 and gcd(a, c) = 1.

A: Consider, gcd(a, b) =1 and gcd(a, c) = 1. If gcd(a, b) =1 then there exist integers m and n such…

Q: Let -2 0 A= -3 1 Find A-, if it exists. 1 2 а) 3 1 2

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Q: Prove: If a &gt; 0, then (1/a) &gt; 0.

A: It is given that a&gt; 0.It is known that if ab &gt; 0 then a &gt; 0 or b &gt; 0 or a&lt; 0 or b…

Q: - BJ -1]. prove prove A²-A-51 = 0 3 If A =

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Q: 9/State the Sufficient condition for the best apfraximation ant Prove t

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Q: show that (ex1 )^x2 = e^(x1 x2) = (ex2)^(x1 ) for any numbers x1 and x2.

A: In order to prove the equations:

Q: Show that (c + V² – x \c – V² - x. + V² – x²) – In = 2 In(c 2 In x

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Q: Let S be any set of non-negative integers with k + 1 elements. Show that there is x, Y E S s.t. k…

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Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 + n², express an in terms of n.

A: In this question, we solve the recurrence relation  in terms of n an=2an-1+an-2+n2witha1=3a2=4

Q: 4] Let x, YER Using proof by contradiction, prove that VxVy(512y3+8x2y<x³+64y2x⇒8y<x)

A: Introduction:   The procedures to be used when employing direct proof to determine a statement's…

Q: integer of the form okts is also but not' conversely

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Q: 1. Prove with the resolution calculus -(PA-Q) -P (RAS) VQ

A: To prove with resolution calculus: ¬P∧¬Q         ¬¬P__________R∧S∨Q

Q: 3. Let, a1 = 3, a2 = 4 and for n 2 3, an = 2an-1 + an-2 -5, express a, in terms of n. %3D

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Q: Prove that: 4 If 2x, 21000 then x, 2 300 or x22 200 or x3 2400 or x4 2 100. %3D1 HINT: Use…

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Q: Find all integer x satisfying the condition x = gcd(5x + 2 3r) lustify vOur ancu

A: The complete solution is in given below

Q: Let a, b, c, d, e, and f be positive integers. Let d = gcd(a, b, c), e = gcd(a, b) and f = gcd(e,…

A: Given that for positive integers a,b,c,d,e,f , d=gcda,b,ce=gcda,bf=gcde,c

Q: State and Prove Pick’s Theorem.

A: Let P⊂ℝ2 be a polygon with all vertices on lattice points on the grid Z2. Let  I be the number of…

Q: ompute the gcd of 11 + i and 61 in Z[i] to find x + yi such that x2 + y? = 61.

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Q: tet A= 2J ndb- -9 12.-6 -6 -4. and let be the Set of all bineaa Corabinationef Callemng of A -the As…

A: A=3-42-912-6-68-4, b=000 (a) Set of all linear combination of column of A w=a3-9-6+b-4128+c2-6-4 Let…

Q: 3. Show that A is positive if and only if A B B for some B.

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Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 +n², express an in terms of n.

A: a1=3, a2=4 n≥3; an=2an-1+an-2+n2 First from the given, the given values shows that the terms are in…

Q: Prove that if a and b are both positive, and a2 < b2 then a < b          (Use Indirect Proof)

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Q: Prove using Direct Proof: For all integers a,b and c if a|b and b|c then a|c

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Q: L) Prove that (3-2)(x+2) = 3 +21 iFitwas

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Q: Let i be a positive integer and A = [-i + 1 ,1]. Then UA,

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Q: Let a1, a2, a3, . .., an be real numbers. Prove that at least one of them is greater than the…

A: We prove it by contradiction.

Q: let 19, b) = 1, them prove that there exists x20 Such that ijzo ax_by = 1

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Q: 2. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 + 5n, express an in terms of n.

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Q: R is commutative if and only if R[x] is Commutative. True or False

A: The given statement is true. If Rx is cummutative.So, R⊂RxRx is cummutative.R is also…

Q: s) Let a and b be positive integers such that b< a < 10b. How many ways are there to place a…

A: In the given problem Balls are labelled and boxes are unlabeled. i.e. we have to distribute a…

Q: Two runners start a race at the same time and finish in a tie.Prove that at some time during the…

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Q: 2. Let, a, = 3, a2 = 4 and for n 2 3, an= 2an-1+ an-2 + 5, express a, in terms of n.

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Q: Let G = Express b2abab3 in the form biaj.

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Q: .

A: The matrix                 A=12-12-12-12-1212-12-12-12-1212-12-12-12-1212 We have to compute A2 and…

Q: Prove that A,(3, 2) = q² for any integer q>2. %3D

A: To prove : Aq3, 2=q2 for any integer q≥2 Pre-requisite : 1. Sphere-covering bound : For an integer…

Q: Consic and b whose divisic demor exist r

A: let R=ℤ-2 function is defined as da+bx=a2+b2 and dxy=dxdy now, for x,y∈ℤ-2  xy-1∈ℚ-2 then, for s,t∈ℚ…

Q: Prove the following statement using the axioms and lemmas For all nonzero real numbers w, x and y,…

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Q: prove that if a>4 then (a-2)^2>4

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Q: Let (a,b)=1 Show that (a+b, a-b)=1 or 2. When is this GCD 1? When is 2?

A: Proof:It is given that gcd(a,b) = 1. So ax + by = 1.Let gcd(a + b, a – b) = d, then d|( a + b) and…

Q: Prove that Q (1 + i) belongs to Q (4-i)

A: Prove that Q (1 + i) belongs to Q (4-i)

Q: Show that det(A) is (a* – b*)/(a – b), where a +b ab A = 1 a +b ab 1 a +b for a and b any real…

A: Given, A=a+bab01a+bab01a+b