Choose the correct definition of from below. O A. kl(n- k)! n! O B. kl(k-n)! k! c. nl(n- K) O D. (n - K)I n! SUBMN + PREVIOUS

Q: 1. If N = 12, k = 8, and n = 5. Find P(2). %3D

A: X follows a hypergeometric distribution with N=12, K=8 and n=5 and k=2 We will use the formula:…

Q: Which of the following statements best justifies In(n+ 1)

A: We are given the following series.               We know that ln(x) < x. So, ln(n+1)/n will…

Q: Prove the following statement by contradiction or contrapositive. Suppose m, n E Z. If m² – n is…

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Q: Find the value for z if P( -z < Z < z ) = 0.7427.     0.37     0.65     1.13     0.33

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Q: There are 3 cnuecutive odd nos such that e The sum of the Lest twe is seven feas than kive tumes the…

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Q: II. Prove S< M2,2. (Write a detailed, logical, well-organized proof.) s = {[6 1:9r - 7s = 0; r.sER}…

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Q: 1. Give a proof of the following statement. 3 integer c > 0 V integers r > 0 3 integer d > 0 : x² –…

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Q: O what docs the con verge to? 2 n teilscoping serics given (ran n+2

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Q: with N=10 so set Of dah lir a popunhon bunoling 160 b) Calcolale the popuhhon Jhndard dernhon.

A: Formula :

Q: Write the letters (a)-(d) in an order that completes an indirect proof of the statement: If n + 6 =…

A: Given statement:                           If :                                 n2+6=32; then n≠5…

Q: [8] Rewrite the following statement less formally, without using variables: There is an integer n…

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Q: 2. If P (n) : "2.4z + 3""" is divisible by k for all ne N" is true, then the value of k is

A: The solution is given below:

Q: Which statement is TRUE? O n3 is superior to nlogn O nlogn is superior to n nlogn is superior to n?…

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Q: 4. 5. For n E N, { x ER | |x-x*|<1/n } is open. UA_n is open where A_n=(n-1,n).

A: To determine: If the given statements are always true, sometimes true, or never true: (4.) For n∈ℕ,…

Q: 13 If E n = 1 Σ -3 -n-1 = 5, then r 10 Select one: True False

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Q: 6.- Evaluate T(au + bữ), considering the following 1 T(ī) = 2, T(5) = , T(ī) 2, a = -1 and b = 2 3…

A: T(au+bv)=T(au)+T(bv)

Q: 10. Given x, y, and z are integers: If x+ y is odd and y+z is odd, then x+z is odd. d e

A: 10) Given statement is false, because

Q: 2. Prove the following using natural deduction. (f) Given A B, show ¬A ¬B (g) Given A- C and B D,…

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Q: 2. Prove the following statement directly. V a, b, c e Z, if a | b and a c, then a | (7b + 4c)

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Q: 7. Prove: Vn,meZ, if n and m are odd, then n·m is odd.

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Q: 3. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 – 5, express an in terms of n.

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Q: Prove the following: P(n,r)=P(n-1,r)+r.,P(n-1,r-1)

A: Recall: P(n,r ) = Prn=n!(n-r)! n! = n(n-1)!

Q: Show that p(x* |¤, S) = stu-t(*Ho+nã n+K n+k+1 (n+k)(n+m+1-d) Eo + (n – 1)S + В.3. K- m +1- d)…

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Q: 1. Let, a1 = 7 and for n > 2, an = " express a, in terms of n.

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Q: The least element of a set {n eN:n- k +1 3 ke N} is (} OA 1 OB. 0 OC 2 OD. None of the mentioned:

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Q: For the following set, specify reasons inf A and sup A; A={1/n:n=1,2,…} .   Tipe : No handwriting…

A: I suggest first plotting a few elements of A on the number line; e.g., 1,1/2,1/3,...... There is no…

Q: Q2/ Apply De-Morgan's theorems to the Following Expression ABC + DEF

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Q: Two pennies, one with P(head) = u and one with P(head) =w, are to be tossed together independently.…

A: Two pennies, One p(head) = u Another p(head) =w We have to tell, Can u and w can be chosen as…

Q: 3. Let, a1 = 3, a2 = 4 and for n 2 3, an = 2an-1 + an-2 -5, express a, in terms of n. %3D

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Q: Prove that the following statements are false: a. The sum of two odd counting numbers is always…

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Q: In the given question as follows, determine whether the statement is true or false. If it is false,…

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Q: 5. Use the diagram below to prove MOOP P. Q

A: Given the diagram

Q: Consider the statement, "If n is divirsible by 30 then is divirsible by 2 and by 3 and 5" which of…

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Q: 2. Rewrite the following sets using list lotation. (Like A = {1,3,5}.) (a) A {r| x is odd and 0<r<…

A: We have to rewrite the given sets using list notations.

Q: 21 Which of the following is equivalent to P(n+1, 3)? O n - n O n? +n O n + 2n – n О Зп + 3

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Q: 3. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1 + an-2 - 5, express an in terms of n.

A: We will solve the problem using recurrence relation

Q: 1. is IS a. proper b. improper C. more than 1 d. equal to 1 e. the same as 7/5 in/7

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Q: 5. Use the method of proof by contradiction to show that the following state- ment is true. Suppose…

A: Introduction: The method of contradiction is a tool to prove the validity of a mathematical…

Q: prove the following P(n,r)=P(n-1,r)+r  ,P(n-1,r-1)

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Q: 45, n-1 on? 12 1 2, ns 1, Al 7(n 11, what is the

A: This is a problem of inhomogeneous recurrence relation and counting.

Q: Prove (without expansion) b a c d a -d = (a? + b? + c? + d?)? d -b -c a |-d -c b a

A: We have to prove that abcd−ba−dc−cda−b−d−cba=a2+b2+c2+d22 Consider the left hand side expression…

Q: 3. No more than 2 have ridden with a drunk driver. P(r s3D 2) .010 4. Exactly 11 have ridden with a…

A: In question, There is part 1 and part 2 already filled with correct answer. So According to bartleby…

Q: For what values of c is ||c(3, 4, 2)|| 1? (Enter your answers as a comma-separated list.)

A: According to the given information, it is required to find the values for c where:

Q: sed on the slot machine shown to the right, in how many ways can we obtain bars on all three whe…

A: The following solution is provided below :

Q: rove the following  P(n,r)=P(n-1,r)+r.P(n-1,r-1)

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Q: if m is even and n is odd demonstrate that m*n= is even

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Q: Given p: n is an odd integer q: n is an even integer. Which of the following statement cannot be…

A: Given statements p: n is an odd integer q: n is an odd integer  The answer can be found by verifying…

Q: for example of anoucommutative take the sel 6as Consisting of the six Puckin Shere we d.fiue R(x): メ…

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