Exercise 8: Let x ER\Z, and suppose x has a finite number of decimal places. Let n be the numbe of decimal places of x. Since x is not an integer, n > 1. Let a be the digit at the n-th decimal place Show that no matter what the value of a is, 3x also has n decimal places. (Proof by cases)

Q: 5. Let n Your-Reg-ID (7 digits number) and = let 21, 22, 23,..., Zn be the (distinct) n-th roots of…

A:

Q: Give an inductive proof of the following identity where Fn is the math Fibonacci number F0^2 + F1^2…

A: To prove  f02+f12+f22+...+fn2=fnfn+1          1 where fn is the Fibonacci number

Q: Find the identity element for the operation * on N defined by a *b=a+b+2, Va,beN al al a 240 does…

A: Let e be the identity element. Hence, it can be written that a*e=a .

Q: let x  be a fixed but arbitrary integer. Do there exist infinity many integer y such that,…

A: Let x = x0 be fixed given integer. Then,

Q: Suppose that n pigeons are placed into m holes with m ≥ k(n+ 1) for some positive integer k. Suppose…

A: See the attachment

Q: 6. Let a be a number written (in base 10) as ao 10⁰+ a₁ 10¹ + a₂. 10²+...+an. 10" where 0 ≤a < 10.…

A:

Q: Let x be an integer. Prove that, if x mod 9 = 5, then 9|(x^2-2x+3)

A: Given: x mod 9=5 then, 9|x2-2x+3|

Q: I need help with this problem and an explanation for the solution described below (Discrete…

A: The objective of the question is to find the negation of the given statement. In logic, the negation…

Q: What does the K stand for in Kn? (Finite)

A:

Q: Kample tetx be Let X€2Z. Prove that for cveri integer n2 , x^is cuen × is aven 2.

A: Yes, for n greater than or equal 2(n is a positive integer) if x is even then x^n will also be even.…

Q: 5. Let r > 1 be an integer such that 2" + 1 is prime. Show that r = 2" for some non-negative integer…

A:

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 S be the set of all real numbers except -1. Define * on S by a*b = a + b + a b. The solution of…

A:

Q: Find all integrs n Such that

A: We have to find all integers 'n' such that ϕ(n)=n3ϕ(n) is a Euler totient function which means ϕ(n)…

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

A: Introduction: Contra-positive method is the way to prove a mathematical statement. Every conditional…

Q: Show that for integers a, n satisfying 0 < a <n, ged(a, n) = gcd(n, n-a)

A: Solution is given below:

Q: Let S, be the set of real numbers such that their decimal ex- pansion contains 3 at l-th place after…

A:

Q: What is Fn * Fn+1 with F representing Fibonacci numbers

A: The objective is to find Fn×Fn+1 where F represent Fibonacci numbers

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 that for every real number x, 3x - 6 ≤ x iff |x-1| ≤

A: The objective is to prove that , where  is a real number.The inequality  is equivalent to .

Q: ↑ Use the following cell phone airport data speeds (Mbps) from a particular network. Find Q₁. 0.1…

A:

Q: Prove that for every positive integer n, there exist i and j with 1≤ i < j≤n +1 such that n is a…

A: Answer

Q: 1. How many elements are in the set {49, 51, 53,..., 177}? >

A:

Q: List all numbers x such that 0≤x<100 and x ≡ [3,1] mod [4,5]

A: Given,           0≤x&lt;100, and  x ≡ [3,1] mod [4,5].

Q: Let A₁ = {1,2,3,..., i} fori = 1,2,3,... 72 Find Ai i=1 An A1 (0,00)

A:

Q: Show that if h+1 distinct integers are, Chasen from the Set El,2,en.,4n}. then there are always two…

A: To show that choosing n+1 distinct integers from the set {1, 2, 3, ..., 4n} then there are always…

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

A:

Q: TRUE or FALSE: 1. There is no integer n such that 4 | (n^2-2) 2. The GCD of all prime numbers is 1.…

A:

Q: Prove that xk = x* mod |G| for x € G for any integer k.

A: Prove it considering two cases.

Q: If a and b are integers with gcd(a, b) = d Then gcd (-- d.

A: Given a statement

Q: . show that for every positive integer n, if n^2+2 is prime then n is a multuple of 3. Is the…

A:

Q: d/ Prove that the following numbers are real (for any 3 享

A:

Q: 15. Use a 30-60-90 triangle to find the tangent of 60°. 2 /60° 1 30% √3

A:

Q: Let {\mathcal S}S be the set of all (nonnegative) 4-digit integers. How many integers does {…

A: Here given S is set of all (nonnegative) 4-digit integers We have to calculate,  How many 4 digits…

Q: Let X-N(65,36) P(x<70)= O 0.50798 none O 0.98077 O 0.76973

A:

Q: (14) Let E denote the set of even integers, O denote the set of odd integers, and x, y € Z be any…

A: I have given the answer in the next step. Hope you understand that

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: 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.