3. If а, 1000". Find N E I, the set of positive integers, such that an+1 < an (n > N). n!

Q: What is the set M of positive integers less than 100?

A: Given statement is set consist all those positive integers less then 100. Collection of all these…

Q: It is known to be Q∼N.Show that QxQ∼N (prove power sets)

A: Solve the following

Q: Prove that the hundreds digit of n20 is even.

A: To Prove that the hundreds digit of n20 is even.

Q: Suppose that you have 19 balls to place into four different bins. Nine of the balls are red, while…

A: Given data: The total numbers of balls are n=19. The numbers of red balls are r=9. The numbers of…

Q: If the first three Fibonacci numbers are given as x, = 1, X2 = 1 and x3 = 2, then what is the least…

A: This is a question of number theory therefore from the subtopic of counting.

Q: Prove dis prove that the or smallest non- commutative ving is of order 4-

A:

Q: 1. Show that subtraction is not associative for the set of integers.

A: Definition :Let "." be a binary operation and A is a setThen "." is said to be associative for A if…

Q: 1. Use a direct proof to show that "If n is an odd number, then n' is an odd number."

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: For an integer n > 1, how many decimal stings of length n begin or end with an even digit? 5(10)"-1…

A:

Q: Suppose that 43% of people own dogs. If you pick two people at random, what is the both own a dog?…

A: Given, Probabily of a person own a dog is 43 %

Q: 8. How many positive integers less than 1000 a) have exactly three decimal digits? b) have an odd…

A: According to our guideliness we can answer only the first 3 subparts. Positive integers less than…

Q: 11. Establish the following relation between Fibonacci and Lucas numbers: L,=u, + 2u,-1

A: Introduction: We know that the relation of Fibocanci number and Lucas numbers is given by  F0=0,…

Q: Let A be the set of positive integers that are less than or equal to 40 and are multiples of 4 and…

A: Given: Let A be the set of positive integers that are less than or equal to 40 and are multiples of…

Q: A non-repetitive list of length 5 is to be E, F, G. The first entry must be either be a vowel. How…

A:

Q: Suppose a set of 8 numbers are selected from the set: {1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13;…

A: It is given that 8 numbers are selected from the set 1,2,3,4,5,6,7,8,9,10,11,12,13,14.

Q: 9. This question is a little more challenging. How many integers in the interval [1, 99 999] (i.e.,…

A: Given data:   The given sum of all digits is k=10. The number of digits that can be used is n=5.…

Q: 14)If the numbers On are and an= 3an defined by a= I , --20- for nz3, faoce that

A: We will first write the given recurrence relation  in homogeneous form then find its characteristic…

Q: a) How many 3-digit positive integers are there with odd digits?

A:

Q: 1.How many license plates consisting of 6 digits (0 to 9) have their digits in strictly increasing…

A: Given that, How many license plates consisting of 6 digits (0 to 9) have their digits in strictly…

Q: Prove that the Ving of ComPelX numbers C¢,+.)is fielol

A: Solution is given as below:

Q: 42 Show that E a Imod n) for all integer aif and only if n is squarefree. Ep(n) is Euler Totient…

A:

Q: 21. How many positive integers x are there such that 3x has 3 digits and 4x has four digits?

A:

Q: If the first three Fibonacci numbers are given as x, = 1, x2 = 1 and x3 = 2, then what is the least…

A: 5. The term “Fibonacci numbers” is used to describe the series of numbers gener-ated by the…

Q: Let n, m, a, b be positive integers. motl Lof oontredietion u th

A: Given, n, m, a, b be positive integers. To prove that…

Q: We need to attempt to find an exact value of n such that  P(r ≥ 6) = 0.98. Clearly to guarantee…

A: We have to fill blanks from given statement Clearly to guarantee at least six people are literate,…

Q: Show that for any nez, n is erther odd or even

A: Suppose P(n) is a given statement, then P(n) is true for all positive integer if: P(1) is true. If…

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

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

Q: 8 of 22 If č = (-3, –5) and d = (-2, –6), find |47 – 2.5d|. V74 O 8/6 O 7/5 146

A:

Q: Let $S = \{25, 30, 35, \dots, 280, 285, 290\}$. That is, it consists of the multiples of 5 from 25…

A: We have S=25 , 30, ...., 290 Now, the first element in the set is 25 and the last element is 290.…

Q: O Prove that G(Vatienal number bers)is negrigibleset

A:

Q: : a number is even  if

A:

Q: Let x, y E N, determine each of following statemen is true or false (N means Natural number, natural…

A:

Q: Let S be the set of all (nonnegative) 4-digit integers. How many integers does S contain?

A:

Q: 9. Show that 1729 is a Carmichael number.

A: To show that 1729 is a carmichael number

Q: of the apples is equal to 3 of the oranges. If there are 12 mor 5 In a fruit stall, - - annles than…

A: Fraction:  A small part of something.  In other words, numerical value that is not a whole number A…

Q: Prove the statement by: a) contraposition b) contradiction

A: Given statement is, “For all integers m and n, if mn is even then m is even or n is even.

Q: If n is an integer greater than 2, then for all integers m, n does not divide m or n + m # nm.

A: c Given n∈Zand n&gt;2. We have to prove that for all m∈Z, n/m or n+m/nm. Suppose n/m and…

Q: 5.) For nzIiecove that teger 1prove 'Dirision Algarithme ncntl) (2ntl16 is an in integer Use the

A: To prove that, for n≥1, nn+1(2n+1)6 is an integer

Q: What is the set of O of odd positive integers less than 10?

A: The odd positive integers less than 10 are 1, 3, 5, 7, 9.

Q: In how many ways oul od class of 32) be chaskn to aitend cenforance, cam 2ostudents

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: How large a subset of the integers from 1 to 50 must be chosen to guarantee that one of the numbers…

A: We have to determine How large a subset of integers from 1 to 50 must be chosen to guarantee that…

Q: 1. Given a deck of 30 cards labelled with numbers 1- 10 (with 3 cards of each number), how many…

A: From the given information,  A deck of 30 cards labelled with numbers 1-10 (with 3 cards of each…

Q: 4. For natural numbers n and k, prove (C) - ()

A: We have to prove

Q: Let S = {25, 30, 35, ., 280, 285, 290}. That is, it consists of the multiples of 5 from .... 25 to…

A: Given that the set S={25,30,35,....,280,285,290} which consists of multiple of 5 from 25 to 290. We…

Q: If geRfabland if hex)=gox) except fos of finive number of number Point in fab?, then prove…

A: The given partition should be first divided into finite partitions.

Q: Let S be the set of positive integers less than 500. Find the number of integers in S that are…

A:

Q: Show that for any neZ, n is either n= 4k n= 4ktI or n=Yk+2 n=4 K+3 or

A: Given below the detailed solution

Q: 4. Give the indirect proof of the statement "if n ie an inkger and n'tl is odd hen n is even.

A: We prove it by contradiction.