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Q: A student claims that he does not need to define permuta- tions because he knows the Fundamental…

A: A permutation is the arrangement of objects where the order of arrangement is considered. The…

Q: Show that = n. mnZ

A: mZ = set of all integers which are divisible by m mnZ = set of all integers which are divisible by…

Q: If ftickiieI{ is acollechion of Subsets ofX then く) andh %3D det the equality not (X;)-( true in…

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Q: is divengent 2) Show that the harmoni series

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Q: If lal = n, show that |a'| %3D gcd(n,t)

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Q: Is the produ ct elementary. matri ces dalways OF two an swer. elementary ? Sustify your

A: The product of elementary matrices need not be an elementary matrix. Recall that any invertible…

Q: Suppose that four microchips in a production run of fifty are defective. A sample of six is to be…

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Q: For sufficiently lazpe n en ns n Zus (en n)

A: According to this question, we know that

Q: 15, If neZ, then nº +3n +4 is even. (Try cases.) ho bn 6. If two integono

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Q: 10. Show that the interval (0, 1) is covered by the open intervals In (1/n, 1- 1/n), n 2 3, but (0,…

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Q: Show that im n /-

A: Limit of the sequence

Q: SA

A: We will understand about the SAS and Donkey Theorem.  SAS :- SIDE-ANGLE-SIDE (SAS) theorem: If two…

Q: Use algebra to find the largest possible value of 8 or small- est possible value of N that makes…

A: 23. This equation comes from the ε,δ definition of the limit. As x→2 the function 3x-1→5. So for all…

Q: If the interval [4,9] is partitioned into n = 5 subintervals of equal length, what is Ax? Ax = (Type…

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Q: Determine for which n ≥ 3, Wn has a Hamilton circuit. Justify your answe

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Q: prove tuat Only Ø ond IR ere open Subsets of IR Mice handwritting will be appreciated!

A: In the given question we have to prove or disprove that ∅ and ℝ the only open subset of ℝ. Note: the…

Q: 10. State the Gödel Incompleteness Theorem. On which school of the foundations of mathematics did…

A: Godel Incompleteness Theorem states that the mathematical ideas should not have contradictions. This…

Q: Oue. 4a) find second degree polyDOMAX. passes through the foimts (0,1), (13), (2,7) and (3,13),

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Q: 11. Let SC R and suppose that s := sup S belongs to S. If u ¢ S, show that sup(SU {u}) = supfs*, 4).

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Q: (3) Find the formula for the number of ways for putting n identical balls into k distinct boxes so…

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Q: Suppose, car name plates have the following format. XXXYYY where the X places should have a letter…

A: Use the given conditions to get a proper answer. Start the question with the possible numbers for…

Q: 2. A round-robin tournament, each team plays every other team exactly once. Use mathematical in- n2…

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Q: 2. How many bit strings(strings of 1 or 0) of length 8 are there such that it contains no more nan 3…

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Q: 8. How many bit strings(strings of 1 or 0) of length 12 are there such that it contains exactly 4…

A: We need to find the number of bit strings (strings of 1 or 0) of length 12 such that it contains…

Q: Assume that (an) and (bn) Cauchy sequences. Set cn = |an – bn|. Prove that (cn) is Cauchy. are

A: Given: an and bn are Cauchy sequences. cn=an-bn To prove: cn is a Cauchy sequence.

Q: What is the minimal number of people needed in a class to ensure that there are two students with…

A: Given information: To ensure that there are two students with the same birthday (the same month and…

Q: Prove or disprove that if {a,} and {b,} are Cauchy and b,n # 0. Then An is Cauchy

A: If an and bn are Cauchy and bn≠0, then anbn is not Cauchy. Result used: If an and bn are Cauchy and…

Q: 1 ient of in al</z] <2 is

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Q: Suppose ZCBA= ZDEA. Using only the information provided in this problem, can you use the SSS…

A: B. By SAS rule only.

Q: How many bitstrings are there of length 2n that contain exactly n “O"s and n “1"s? Prove your result

A: Given that,   The length of bitstring =2n, i.e If we have a bitstring, it should only contain 0's…

Q: 3 In how many ways can you chocose 6 cocolakes from 10 diferent types f there are more than 6 of…

A: Since there are more than 6 of every type, except type 5, so consider the number of chocolates as…

Q: (3) Recall that a lattice path on the grid from (0,0) to (n, n) can be viewed as a sequence of…

A: Given: To show that Cn,  is equal to the number of ways of placing n unlabelled ball in n labeled…

Q: Let it be S={ ujuP alinearly in dePendent SEl

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Suppose a password must be express by selecting digits for 5 places, the allowable digits being 0,…

A: Although, the example of a typical password is 332401, a 6 digit number, the first sentence of the…

Q: 3. Suppose (a,n) is Cauchy and that for all m, k 2 100, Jam - as 0. Does it follow that the…

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Q: An organization wants to assemble a cluster of n computers using wires and hubs. Each must have…

A: Solution of the problem as follows

Q: A. The number of permutations of length n that avoid 132 and have the additional property that their…

A: Based on the additional property, the first entry is larger than the second entry is Cn-1, (the…

Q: Show by means of a membership table that both absorption laws are identities.

A: According to the given information, it is required to show that the absorption laws are identities…

Q: The Pauli Exclusion Principle tells us that no two electrons in an atom can have the same four…

A: Please see the below picture for solution.

Q: what about Fini'te in Finite or in tersection of Par tition of [a,b] Did it is 1 gais partition not…

A: A partition P of Z is a set of non empty subsets of Z such that every element p in P is in exactly…

Q: Suppose a die is cast 10 times. Let X1 be the number of terminations in the set {1, 2}, X2 be the…

A: Let us assume X1 denotes {1,2} faces show in 10 throw . The probability of that will be P(X1=1 and…

Q: Write down all even permutations of {1,2,3,4} which take the element 1 to 2.

A: To write all even permutation of A={1, 2, 3, 4} that takes 1 to 2.

Q: Suppose a fair coin is flipped twice. Let A1 = "Head on 1ª Toss" Az = "Head on 2nd Toss" Ag =…

A: Given: A1 = Head on 1st toss A2 = Head on 2nd toss A3 = Exactly one head. Sample space = {HH, HT,…

Q: Is f(x, y, z) = 8 In x+7 In y+5 In z homothetic? Of(x, y, z) is not homothetic Of(x, y, z) is…

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Q: Select all symbols that are allowed to go in hypotheses statements (even if it was not covered in…

A: We know that in a hypothesis statement, we use different symbols for the different hypothesis tests.…

Q: How many bit strings of length greater than equal to one and less than or equal to six are there?

A: There are 2 possible bits : 0 and 1 Bit strings of length 6 are, 2.2.2.2.2.2=26=64 Bit strings of…

Q: 8. Following the idea of Exercise 6 and referring to Exercise 7, express the positive gcd of 49,349…

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Q: For what values of aand b is {u, v} an orthonormal set?

A: A set of vectors form an orthonormal set if all the vectors in the set are mutually orthogonal and…