Suppose a, ne Z and 0 < a

Q: What are the possible number of Boolean functions with n-ternary variable?

A: We have to state the possible number of boolean functions with n-ternary variables.

Q: Suppose that n pigeons are placed into m holes with m ≥ k(n+ 1) for some positive integer k. Suppose…

A: See the attachment

Q: Suppose r is a non-negative real number and n is a natural number. Use the Binomial Theorem to prove…

A: The binomial theorem states that for the positive integer value n: x+yn=∑k=0nCknxk+yn-k

Q: Compute the following: (a) 4!, (b) (), (c) (₂), (d) (), (e) (7), (f) (2)-(2) where n is a…

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Q: Let P(x) be the statement "x^2−x−20⩽0". a. If the domain consists of −4,0,1 and 2, then "∀x,P(x)"…

A: Given: Here is the given statements, 1. Px=x2−x−20≤0 To find: Is it true or false that "∀x,P(x)" is…

Q: 1a) suppose that f is defined recursively by: f(0) = 5 and f(n+1)= 2fn + 5. Find f (1) f(2) f(3)…

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Q: 2. U={x|x is an integer, 2<x<10}. A and B are subsets of U such that A= {multiples of 3}, B={factors…

A: Using set theory we have to answer following.

Q: Using the generating function to determine the number of ways  18 identical balloons can be given…

A: Given that 18 identical balloons can be given to 3 children such that each child receives at least 5…

Q: Suppose that the number of subsets with k elements, made out of a set of n elements is called by the…

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Q: 2 4) The graphs of y=x and y=x make it obvious that x >x for all real number x > 1. Use induction…

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Q: Consider the question: Apply five iterations of the Gauss-Seidel method, with initial approximation…

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Q: Prove that for all integers n.4n² +6n + 1 is not divisible by 4. Be sure to explicitly show how each…

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Q: E(3k? – 2k + 3(-1)k)

A: Given,  ∑k=110(3k2-2k+3(-1)k)

Q: If there are a total of 8 chocolates be given to to three children such that each children receives…

A: Given: 8 chocolates  are to  given  to 3 children such that  each children receieves at least two…

Q: Show that =- 5)" /31 + 6. 1 = 2 ) /7! + () /9! – ... %3D | -- IN

A: We know that, from the Taylor's formula for power series expansion of sinx is given as…

Q: (10) The following element is prime in (Ze,+,.) = .... .. (а) 2 (b) 4 (c) 12 (d) No Choice (а) (b)…

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Q: [a, b] = N=1 (a -,b+-) To prove this, show the following: То Show that [a, b](a – ÷,b +- ) for every…

A: Given that, [a,b]=∩n=1∞a-1n,b+1n This can be written as, ∩n=1∞a-1n,b+1n=[a-1,b] The aim is to show…

Q: How many permutations π of [10] satisfy π^5 = 1?

A: The given set is 10=1,2,3,…,10. Therefore any permutation π of 10, is bijective function from the…

Q: 3. From Fermat's theorem deduce that, for any integer n 20, 13| 1112+6 + 1.

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Q: 11. (a) What does the symbol n! mean? Find 5!. (b) Define (), and find (2).

A: To find 5! and to find the value of 52

Q: prove the following identities k(nk) = (n-1k-1) (n0)+(n1)+(n2)+ .... ..... +(n n-1) + (nn) = 2^n…

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Q: Show that /(-1)-7(1) but there is Let f(x) 1 Show that /(-1) (1) but there is no number e in (-1, 1)…

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Q: Find all 6 permutations of (12)(345).

A: Find all permutations with 12 in the first pair of bracket : (12)(345) (12)(354) (12)(435) (12)(453)…

Q: Find a Big-O estimate of (2n+n2)(n3+3n)

A: Given the given expression is 2n+n2n3+3n. Big-O notation: the fn is Ogn for positive constant C and…

Q: (A) = and (B) = . Find 2A - BO* none of the above

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Q: prove that (1- (1/4))(1-(1/9))(1-(1/16))...(1-(1/ n2)) =(n+1)/2n for all integers n greater than or…

A: We have to prove that  (1- (1/4))(1-(1/9))(1-(1/16))...(1-(1/ n2)) =(n+1)/2 By mathematical…

Q: are 51 software students taking Let pi, p2,.. Psi be their final cam scores. Hence, cach p, is an…

A: Given that p1, p2, p3,..., p51 are the final exam scores of 51 software students who are taking MATH…

Q: An urn contains m number of red balls and n number of white balls. Two balls are selected without…

A: Solution-: We have given there are 'm' number of red balls and 'n' number of white balls We want to…

Q: g) Determine the product of Factorial of 5 and Fibonacci of 5 using the recursive function as…

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Q: Let F(n) denote the Fibonacci numbers. Prove the following property for n ≥ 3 directly from the…

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

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Q: (a) If a, b,c € Z+ and a +b=c then (c,[a, b)) = (a, b).

A: As you asked multiple questions , so I solved only the first one.

Q: A scientist noticed that the population of a certain country could be represented by the following…

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Q: 1) What are the values of C and k of the term Cykx20 in the polynomial expansion of (x² + y )100? 2)…

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

Q: 1.- Let x* be defined as one more than the number of digits in the integer x. For example, 150* = 3…

A: topic - linear equation in one variable

Q: The sum of the entries in the nth row of Pascal's triangle is equal to 2"1 for each n e N. Proof:…

A: Here we will check whether given statement is true or false,

Q: n + 5 > 4 n

A: We know, the square of an integer is always non-negative (n - 2)² ≥ 0 for all integers n

Q: Suppose U~ Select one: Binomial(n, p) and n > 2. What is P(U > 1)? a. (1-p)"-¹[(1 − p) + np] b.…

A: Given that, U~Binomial (n,p)

Q: For q > 1 and the positive number "n" and 1≤d≤n ٫ Prove : Aq ( n , d ) ≤ q^(n-d+1)

A: It is given that For q &gt; 1 and the positive number "n" and 1≤d≤n

Q: 10. By Binomial Theorem (2a – b)* =16a* – 32a’b+24a*b? – 8ab³ +b* | a. TRUE. b. FALSE.

A: We know the binomial therom expansion