Computations In Exercises 1 through 6, determine whether the binary operation gives a group structure on the given set. If no group results, give the first axiom in the order G₁, G₂, G3 from Definition 4.1 that does not hold. 1. Let be defined on Z by letting a*b = ab. 2. Let* be defined on 2Z = {2n|n € Z} by letting a b=a+b. 3. Let * be defined on R+ by letting a + b = √ab.

Q: Determine L-1) 9s – 8 (? – 2sJ*

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Q: Find L[et tsin(2t) - e-2t+3 +e-2t cos 3t]

A: BY USING THE LAPLACE TRANSFORMATION RULES  WE GET OPTION (D) IS CORRECT OPTION.

Q: Let A = {4n^2 + 1|n ∈ Z}. Show that A is a subset of Z but not equal.

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Q: Let {(=) = In ="(z +2)*(z² + 9)] f'(x) =

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Q: Let P(x) be the statement "x^2−x−20⩽0". a. If the domain consists of −4,0,1 and 2, then "∀x,P(x)"…

A: Given: Here is the given statements, 1. Px=x2−x−20≤0 To find: Is it true or false that "∀x,P(x)" is…

Q: Find all n ∈ Z for which 3x^2 + 2nx + 12 is irreducible over Q.

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Q: find the amount of odd three-digit numbers that can be created. (

A: here given digits are  [0, 1, 2, 3, 4, 5, 6]. so there are total 7 digits . here use counting…

Q: Prove that for a # -1, a>0,n EN IS (1+a)^ n >=1+na.

A: Here let A=(1+a)n, a≠-1, a>0, n∈N and B=1+na

Q: Show that 8.

A: A∞=Max∑j=1naij  for i=1 to n=maximum row sumA*=AT=ajiA*1=Max∑i=1naji  for j=1 to n=maximum column…

Q: Let x be the set of all positive integers and d(min) = | = - = | show that (x,d) is not complete

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Q: [a, b] = N=1 (a -,b+-) To prove this, show the following: То Show that [a, b](a – ÷,b +- ) for every…

A: Given that, [a,b]=∩n=1∞a-1n,b+1n This can be written as, ∩n=1∞a-1n,b+1n=[a-1,b] The aim is to show…

Q: Let & € N. Prove by using the contra-positive that if ³ is odd then is odd. Proof: Choose which of…

A: Introduction: The basis for proof by contra positive is the idea that an implication equals its…

Q: Prove that 1+r+r^2+...+r^n=(1-r^(n+1))/1-r for all n in N when r doesn't equal 1.

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Q: Assume that M = N,(h) + k,h+k,h2 + kgh + k,h +.Then using Richardson's extrapolation N(h) is of :…

A: The series in the Richardson's extrapolation is given by the formula . Here, t is the positive…

Q: Show hat + £ +} + - - +$ is out entges

A: Given The given statement is that 1+12+13+· · ·+1n is not an integer.

Q: Give an example of a closed subset S of R^2 such that conv S is not closed

A: An example of a closed subset S of R2 such that conv S is not closed is given below.

Q: Prove that lor n {k=1 positive unteger every K2K = (n-1)2²+¹+2

A: answer is in next step.

Q: of the form {((-1) Cnt1)) (nul) / (nt!)} where Let be the set of humbers A is </ement of the wet of…

A: Given that S is the set of numbers of the form -1(n+1)(n-1)(n+1), where n is an element of the set…

Q: Prove that If P(A) > P(B), then P(A/B) > P(BIA)

A: The conditional probability is defined as P(A | B) = P(A and B)/P(B),  P(B | A) = P(A and B)/P(A)

Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

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Q: . Let n be a positive integer. Prove that 1 · ( n/ 1)  + 2 · ( n/ 2)  + . . . + n ·  (n/ n) …

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Q: d) limnoo 1 •k=1 an e) limn 1 48x = =공 6 4

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Q: Prove that there exists an n ∈ N such that 7 | (3^n − 1).

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Q: Show that the set A = {n^2/ (n+1): ne N} is unbounded in R.

A: To prove that the set A={n2n+1:n∈N} is unbounded in R,

Q: Prove that 3! 2(n+3) = n r=0 (-1) n "Cr r+3 Cr

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Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

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Q: Ifx+y+z= 1 and x, y, z are positive, then show that ( 1)² ( 1)² ( 1)² 100

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Q: Assume a1,a2,...,an are positive numbers, a1+a2+...+an=1. Prove: Please use non-calculus method)

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Q: Let a be a positive real number such that a +1/a is an integer. Use strong induction to prove that…

A: Let a be a positive real number such that a+1a is an integer. Use induction to prove that, an+1an is…

Q: Find the order of 175 in Z_245

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Q: Let A, BeM,(C). Prove that for every integer k21, tr(AB) =tr(BA) Does tr(AB) =tr(A*B* )? Explain…

A: We will do both these subparts of this question for you. Solving this question requires basic…

Q: prove R is not homomorphic to R^2

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Q: · (b + c) = a · = a · b + a · e for all a, b, c € R³. . 7. Prove that a.

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Q: Let A = {4n^2 + 1 | n ∈ Z}. Show that the size of A is equal to the size of Z≥0. Z≥0 is the set of…

A: A set A is said to be countable  if there is a bijective map between A and set of natural numbers .…

Q: (-5) + 4 – 1+ 4- (-21) * (-7)) ova

A: Simplification

Q: why/where/how does the 1 and the 0 about from at the end of the last few steps?

A: By Leibniz rule for differentiation under integration sign is given by, Here we need to…