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 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: determine the value of c(n,5) /p(n,5) where n can be any integer thats 5 or greater

A: Recall the following. Permutations Number of permutations of n things taken r at a time: pn,r=n!n-r!…

Q: 5. Prove that, for n> 1, n

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Q: prove that for all integers m, n & d if d/m & d/n then d/(2m+3n)

A: We know that if a and b are integers such that a/b then b is a multiple of a. i.e. b=ka where k∈ Z{…

Q: Prove that 1+1=2

A: To prove: 1 + 1 = 2

Q: Use a combinatorial argument to prove the following equality: (C) · k = =n(") k-

A: A combinatorial argument or proof is an argument that involves counting. Here is the proof.

Q: (2n- 2. Give a combinatorial argument to show that k- ways the number of ways to select a committee…

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Q: Find 1 (9) Lp(p – 1). p(p²-1)3 (10) L-1 (p2+1)2,

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Q: Prove an+1 = (an2+ 1) / 2 with a1 = 2 is monotonic increasing.

A: Solution:-

Q: The sum of the first n natural numbers, S = 1 + 2 + 3 + first n natural numbers is 171, determine…

A: Consider the given information:

Q: Let p, q, and r be prime natural numbers with p # q and n= p2q. Then, all the subfields of GF(r")…

A: Answer: Option (C) Given that, p,qand r are prime natural numbers and n is positive integer. Let F…

Q: 6. (i). Prove that every prime > 3 is of the form 6m +1 or 6m + 5.

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: To show that the general factorial function: a+ ***** (a)mn = M -~-(-). (+¹)-(+--¹). m here m is a…

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Q: Indicate the least integer n such that (3x5 + x²)4 = 0(x¹). E

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Q: A positive integer n is called superperfect if ơ(ơ(n) = 2n Show that 16 is superperfect.

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Q: 7. For n ≥ 1, verify that 12+32 +52 ++ (2n- +3²+5² · + 2n-1)² = (2n+1) 3

A: Ans : page 1:Ans page 2:

Q: Show that yn for all n=1, 2₁- ✓

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Q: Prove that if n = nxn-1 holds integer value of -n, which means that for a positive integer value n,…

A: We have given that ddxxn=nxn-1 for any positive integer n. We need to show that, ddxx-n=-nx-n-1. We…

Q: п(п + 1) Show that , k 2 k=1

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Q: Give a combinatorial proof for the identity 1+2+3+..+n= (",").

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Q: which pair of binomials disproves Eric's ㅇ (z-2)(z + 3) ㅇ (z-2) (z + 2) z+3)(3 2)

A: Solution:

Q: 7. (a + b)"= E=o( n choose k) a™-kb* for any integer n>=0. Use this theorem to compute (2x-3)* ) The…

A: Given, 2x-34

Q: [1+3* 1- 3k] prove that AK = 1- 3* 1+3*] |1– 3* 1+3% | - 5. For A = -1 2

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Q: Let n ≥ 1, x be a real number, and x ≥ −1. Prove the following statement using mathematical…

A: The principle of mathematical induction is a technique or method that is used to prove the statement…

Q: Suppose A = {2, 5, 7, 9, 13, 25, 26}. (a) Find n(A).

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Q: Q6 A periodic function f (x) is defined as the following function: -n <x<-- S(x)={1 <x<A 2 and S(x)=…

A: