Consider the sets A = {5n+3 | n ≤N}, B = {3n+2 | n ≤ N}. (a) List three elements in A. (b) List three elements in B. (c) Is it true that AC B? And is it true that BCA? Can you explain why? (d) How many elements do you think there are in AUB? Can you explain why you think so? (e) How many elements do you think there are in An B? Can you explain why you think so?

Q: Which of the following rules is used to find the number of positive integers less than 1000 that are…

A: To Determine: which of the following rules is used to find the number of positive integers less than…

Q: In the following, state whether A = B or not:(i) A = { a, b, c, d } B = { d, c, b, a }(ii) A = { 4,…

A:

Q: 5. What is the order of each of the following permutations? a. (124)(357) b. (124)(3567) d.…

A:

Q: 6. Let r> 2 be an integer. Show that R(2r, 2r) > 2

A:

Q: (d) D= {n €Z:n −3} (e) E = {}\{}

A: Here we have to find the set D and E in list form.

Q: In a race in which eight automobiles are entered and there are no ties, in how many ways can the…

A:

Q: a) Is (−3)! possible? Explain your answer.  b) In how many ways can you order an empty list or zero…

A: a.(-3)! is not possible only the factorial of whole numbers are possible. Main use of factorial is…

Q: I n the game of poker played with an ordinary deck of 52 cards various five-card holdings are given…

A: Let me explain what each factor in the expression represents in terms of selections from the deck of…

Q: 15 P5 X 1O! can be written as: 10! 15! x 5! O 10! x 10! O15! 15! x 5! caer

A:

Q: (15) Let a, b = Z. Prove that if a is divisible by 4 and b is divisible by 4, then: (a) ab is…

A:

Q: Prove or disprove: For all sets A, B, we must have 24A2(AAB) = 2B.

A: Given, 2A∆2A∆B

Q: Read the proof below. If the numbers given in the second sentence are {42, 43, 55, 74, 96, 127,…

A: According to given box model, Box number 0 1 2 3 4 5 Last digit 0 1 or 9 2 or 8 3 or 7 4 or 6 5…

Q: Using the fact that "a countable union of countable sets is countable", show that the statement that…

A: Please see the below picture for detailed solution.

Q: 10 Different People order 3 donuts each, chosen from 5 types of donuts. At least one person chooses…

A: (a) Thee will be 10 different possibilities for number of person to pick all 3 donuts of the first…

Q: How many arrangements are there for the letters of the word "PIKACHU" with the CH together in the…

A:

Q: a) Is {5} ∈ {1, 3, 5}?   (b) Is {5} ⊆ {1, 3, 5}?   (c) Is {5} ∈ {{1}, {3}, {5}}?   (d) Is {5} ⊆…

A: A⊆B if every element of A is in B. ∈ - belongs to relation between element and set .

Q: (1) A grocery store sells five types of fruit, called Fruit 1, the number of ways that Alice can buy…

A:

Q: (c) Every element in the set {0, 1, 2} is greater than or equal to half of its square. i. Original…

A:

Q: A: B: C: A U : 18 AnBnC: B An (CUB): 11 10 14 20 How many elements are contained in each of the…

A: Given sets is

Q: | Suppose you have a well-shuffled deck of cards (A.2,...„J,Q.K). a) How many cards would you have…

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: For all integers a consider the following statements (A) 6|a - a (B) 6|a + a (C) 6 a – a +1 (D) 6|a…

A: We have to check

Q: Use the following sets: A={Factors of 50} B={odd numbers} Which elements are found in A∩B?

A: A={Factors of 50} = { 1,2,5,10,25,50}  B={odd numbers} ={1,3,5,7,9,11,......}

Q: How many 4-element subsets containing the letter A can be formed from the set {A, B, C, D, E, F, G}?…

A: Number of 4 elements subsets containing the letter A from the set {A,B,C,D,E,F,G} is equivalent to…

Q: 4. Use a combinatorial argument to show that () n 1 -2) n + 22 n 2 3 -

A: Given: nn-2=n3+12n2n-2n

Q: Answer 5-8 based on the table below. Yes No Teachers 12 20 Students 45 23 5) P(teacher | yes) 6)…

A: