(5) Let A be the set of all real numbers in the interval (0,1) vehose decimal expansions contain only the digits "0" and "3". For example numbers 0.3, 0.03, 0.0300 303,... etc are in the set A, whereas 0,0300403 is not in the set A. a) use diagonalization process to explain why A is not a countable subset of (0,1) b) List an infinite number of rationals that are in the set A

Q: Prove that 7^n − 1 is a multiple of 6 for all n ∈ N. ( N is Natural Number)

A: Advance maths

Q: Find all possible digits that can be placed in the space so that the numbers is 1,182,1_4

A: Apply the rule for a number divisible by 9.

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: Find all Pnterers x such that 5x=12 (mat) LoxE 4 (mad) 7x=16 (modlo) and 1o00s x3000

A:

Q: Assume an unlimited supply of coins worth 5 cents and 9 cents. Prove that some

A:

Q: Find a recursive definition for the set of all integers which are greater than or equal to 15.

A: Sequence is defined as an arranged element that satisfies some definition. Sequences are many types…

Q: 1 101101, and 101, 2. 10111102 and 102 and 112 3. 1000012

A: Since there are multiple questions the first question is answered as per our guidelines. Kindly…

Q: Prove or disprove the following statement: There are prime numbers a, b, c such that a^2+ b^2= c^2.

A:

Q: Suppose a is an integer. Prove that if a^3 is a multiple of 3, then a is a multiple of 3.

A: Let a3 is a multiple of 3 but a is not a multiple of 3.a3 is a multiple of 3Therfore, 3 divides…

Q: How many divisors does (1000000! + 1) have that are less than 1000000?

A:

Q: Prove by cases For any integer n, n^2 + 5 is not divisible

A:

Q: Prove that for all natural numbers n, (n^3/3) + (n^5/5) + (7n/15) is an integer

A:

Q: Let k be an positive integer. Prove that k(7k^2 + 5) + 6 is divisible by 6

A: Let k be an positive integer. Prove that k(7k^2 + 5) + 6 is divisible by 6

Q: Plot the surface z = x+y with a finer mesh (of 0.25 units in each direction),using [x,y] = meshgrid…

A: MATLAB is a computer language that engineers and scientists use to study and build systems and…

Q: {m belongs to all integers| m^2=3}    Now list the elements in the set?

A: The given set is {m belongs to all integers| m2=3}.To list down the elements in the given…

Q: Prove that among 7 positive integers, there are always two integers such that either their sun or…

A:

Q: Prove that for all natural numbers k, a (4^k - 1)/3 + 2*a*4^k is of the form 1 + 6a

A: We show that the question doesnt hold for a=1 and k=1

Q: Which of the following gives the Binet form of the nth Fibonacci number? O Fn = Fn = Fn = Fn =…

A:

Q: Show that given any particular real number, such as I, there is NO next real number immediately…

A:

Q: Show that the weighted arithmetic mean of first 'n' natural numbers whose weight are equal to the…

A:

Q: One of the striking properties of Fibonacci numbers is that gcd(Fm, Fn) = Fd, (*) where d = gcd (m,…

A: 1. We see,        F9 = 34    [Fibonacci series : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,. . . . . ]…

Q: let s be positive integer, then (2) + (;) = %3D

A: sC5 = s!/5!*(s-5!) And sC6 = s!/6!*(s-6)!

Q: Prove that 80

A: Let An=-1n,2+1n and A=∩n=1∞-1n,2+1n=a,b Since, Ai⊃Aj whenever j<i, we can find A by simply taking…

Q: H3 a a Hexadecimal H2 C to d. 7 segment e converter Но g DP

A:

Q: Z+ as follows: For a, b € Z+, a*b = a - b + 1. Z+? Explain. (3.1) Define an operation * on Is * a…

A:

Q: write a program to evaluate even numbers for [1,10],and [11,20]respectively in matlab

A: Even numbers for [1,10] is given below-

Q: Show that there is exactly one real number t such that eTt + te" 207 + V2021.

A: Let us take an equation: g(x)=t Where g(x) be any function of x In order to show existence of x such…

Q: Please provide justified answer asap:::: Show that n is odd if and only if n^2+4n+1 is even.

A:

Q: Let the binary operation *

A: Given,          a*b=a+2b where a and b are real numbers

Q: Show that Consider the Fibonacci numbers {F} defined by F₁ = 1, F₂ = 1, and Fn+2= Fn+1 + Fn. - Fn =…

A: Introduction: In mathematics, a recurrence relation is a significant connection that expresses the…

Q: Give a recursive definition for the set of all the positive integers that are less than 100 and not…

A: Given: Set of all positive integers that are less than 100. To find: Recursive definition for the…

Q: 1. Prove that for all numbers of k, (5*2^(2k+1) - 1)/3 is an odd number.

A: Let the given statement is        For k = 1 we get this as    is an odd number…

Q: how: For all integers and , if n-m is even then  n^3-m^3  is even

A: We have given that for all integers n,m (n-m) is even.

Q: Prove that 18000 + 28000 38000 Theorem (and not a calculator). 18000 + 58000 + +4° 8000 is a…

A:

Q: Prove that n-5 is odd iff n^2-1 is odd

A: Please check step 2 for the solution.

Q: Use the PMI to prove that 6" – 1 is divisible by 5 for every integer n > 0.

A: To prove that 6^n-1 is divisible by 5 for every integer greater that or equals to 0.