If a set S has n > 3 elements, how many subsets of S have more than one element, but less than n elements? 2"-1-n 2"-2 O None of these. 2"-2-n ○ O(n,1)+...+O(n,n-1)

Q: 13. Recall Z = {..,-2,–1,0,1,2,..} (the integers). Let Z* = {1,2,3,.} be the positive integers. Let…

A: Given: ℤ=…, -2, -1, 0, 1, 2, … and ℤ+=1, 2, 3, …

Q: Exploring permutations.  The formula for the number of ways to arrange n objects is n! =…

A: No. of parking spots =5 No. of people =5

Q: Prove the following statement: For all integers x and y, if x and y are even, then 3x + 5y is even

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

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Q: Suppose ʼn is a positive whole number. Simplify [n+1)! — n! × n. On! O 1 On + 1

A: 'n' is a positive whole number. We have to solve  (n+1)!-n!×n Remember : n!=n.(n-1)........3.2.1

Q: n If E (ak + bk) 2n and n+1 k=1 E(ak – br) +, then ak = n n+2 k=1 k=1 3 2 5 2 O None 2

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Q: A number n is divisible by 12 if it satisfies ∃k ∈Z(n = 12k) Give a direct proof that, if n is…

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Q: . Prove the following statement: For all integers x and y, if x and y are both even, then xy is…

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Q: 4. Find the union and intersection of these families, and prove your answers. (a) A = {A, ne N},…

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Q: How can you represent the set {(1, 3),(3, 1),(3, 3), (1, 1)}? (choose all correct answers - there…

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Q: QUESTION 7. Find the number of permutations of length 9 that satisfy the following conditions: (i)…

A: To find- Find the number of permutations of length 9 that satisfy the following conditions: It…

Q: 5. Let r,ne N. Show that the product (n+1)(n+2)...(n+r) of r consecutive positive integers is…

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Q: k = 4 4. Let k be the second smallest nonzero digit of your Student ID. Compute the order of (k, k)…

A: To find the order of (4,4) .

Q: IV. Prove the following using mathematical induction. 1. 5" – 1 is divisible by 4, Vn € W. 2. 8" –…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: The number of the element(s) of order 2 in Z3 O Z6 O 2 3

A: Given  ℤ3⊕ℤ6

Q: Q1: For A = (-3,-2, ... , 4} and B = {1, 2, . .. , 6}, determine S = {(a, b) e A x B: a+b² = 25}.

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Q: 1 A student has to answer 10 out of 13 questions in an exam. How many choices has he (i) if there is…

A: Note: “Since you have posted multiple questions with multiple sub-parts, we will provide the…

Q: n- 5. Use the Vandermonde identity to show that (²₁)-(:)(:1). k=0 Hint: Using central symmetry,…

A: We are given the Vandermonde identity is n+ml=∑k=0lnkmk+m-l. We have to show that…

Q: If x[n]= {2,0,3,4}, x[(n-2),]= O a. {3,4,2,0} O b. {3,0,2,4} c. (2,4,3,0} O C.

A: The sequence is xn=2, 0, 3, 4. Then,  x0=2x1=0x2=3x3=4 Now, consider the sequence xn-24. Then, we…

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Q: 3. Suppose b > 1 is an integer. The proof of the existence of a base b representation of any integer…

A: (a)

Q: Write a (formal) proof of the following statement: "If 4 does not divide an integer n, then does not…

A: Here we have to prove if 4 doesn't divide an integer n, then 4 doesn't divide n2 -3n+5.

Q: Given an integer n 2 1, how many decimal strings of length n begin and end with the same digit?…

A: Given an integer n≥1 We have to find the number of decimal strings of length n begin and end with…

Q: a)Show by one combinatorial method that: 2 2 n C) - () - (") 2n +... + 2 n

A: Given information: The following identity is provided: n02+n12+n22+................+nn2=2nn It is…

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Q: Find, if possible, the number of elements in sets A, B, and C using the given information. n(A-C)=11…

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Q: Let [399] = {1, -.., 399} Find ie(399]|

A: Since you have posted and needed answer for multiple questions  but we can answer one question. So,…

Q: Which of the following statements is true: For all integers a, b, and c, a | be if and only if a | b…

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Q: 1 If the N(A) consists of all multiples of x = , then the rank of A 4 is: а. 3 O b. 2 O C. 4 O d. 1…

A: It is clear that from N(A)

Q: The value of (n + 1)! is O (n +1) - n! O n- (n+ 1)! O n- (n – 1)! O (n +1) · (n+ 1)! O none of the…

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Q: Show that r(r+3) Hence, Show that 1 +. 2.5 1 1-4 3-6 n(n+3) n+3 n+2 n+1

A: Using series

Q: Number of Families Magazine Who Subscribe 23,420 24,130 R 25,570 In a certain town each of 52,160…

A: please see the next step for solution

Q: Which of the following is an example of an empty set? O {x: x€N,4 sx s 5} O The set of odd natural…

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