Suppose A C B, a E A, and a ¢ B – C. Prove that a E C.

Q: This homework problem is part of Math Optimization class.

A: The provided demand equation is given by

Q: Consider the following postfix representation of an expression composed of letters and the addition,…

A: Given: Postfix expression: AB+CD-E*F+* To find: Infix expression of the given postfix expression.

Q: Two different factories both produce a certain automobile part. The probability that a component…

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Q: 1 3 1 3 (b). Given A =-1 4 and B = -2 8 2 5) 0-1 (i). State the sequence of elementary row…

A: Row elementary operations will be used to reduce the matrix from A to B. As per our guidelines, we…

Q: A third-order homogeneous linear equation and three linearly independent solutions are given below.…

A: We have to find the particular solution y(x).

Q: 6. Solve the following system of two linear differential equations. У1 = 5y1 - 2у2 Y2 = 6y1 - 2y2

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Q: Prove by induction that (1)1! + (2)2! + (3)3! + ... + (n)n! = (n where n! is the product of the…

A: A mathematical proposition is given.Let P(n):1.1!+2.2!+3.3!+...+n.n!=(n+1)!-1.Here, P(1)=1.1!=1 and…

Q: 2. If xER and 0<x<4, then 21.

A: In this question, the concept of proof using contradiction is applied. Given, If x∈R and 0&lt;x&lt;4…

Q: The grain food company produces a grain food called Fortified Munchies, which is advertised as a…

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Q: Problem 5.3 Prove that n(n+1)(2n + 1) (3n² + 3n – 1) 30 j=1 whenever n is a positive integer.

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Q: Compute the following (finite or infinite) sums. (a) 17+ 20+ 23 + 26 + · · · + 200 (h) 2+2(1.1) +…

A: We will find out the required value.

Q: 2) Stampy the Elephant and Pixie the Mouse buy a new house for $450,000. Their home appreciates 1.5%…

A: Given data is : House cost is $450000 Home appreciates 1.5% every year , therefore r=1.5%

Q: The counterexample of A = {1} and B = Ø disproves which of the following statements where P(X)…

A: Given that A=1,B=∅. For (a). PA∩B=P1,∅∩∅=P∅=∅ And, P(A)∩P(B)=P1∩P(∅)=1,∅∩∅=∅ Hence statement of (a)…

Q: For each of the following groups, find the order of the group and the order of each element in the…

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Q: 3) For Boolean matrices X and Y, under what conditions does X V Y = X ^ Y? = Consider the 1 × 1…

A: Boolean matrices X and Y.

Q: Provide a complete CFG G = (V, T, S, P) that generates the language L = {xy | x E {a, b}*, y = {c,…

A: The given of the question is the language L, which is defined as the set of all strings of the form…

Q: Use induction to prove that the product of any three consecutive positive integers is divisible by…

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Q: R.4. Prove that for every integer n, n³ is even if and only if n is even.

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Q: Let a, be the nth term of the sequence 1,2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,…

A: Let an be the nth term of the sequence 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6… constructed by…

Q: Provide a complete CFG G = (V, T, S, P) that generates the language. L = {12n|n>0}.

A: The given in the question is the language L=12n|n≥0 which is a set of strings consisting of 1's,…

Q: 6. Suppose f :Z→Z is defined as f = {(x,4x +5):x € Z}. State the domain, codomain and range of f.…

A: From the definition of a function it follows that ℤ is the domain and codomain of f.

Q: 3. Let A = {3k : k € Z} and B = {15m + 12n : m, n € Z}. Prove that A = B.

A: Let     A = {3k : k∈ℤ}    and          B = {15m+12n: m,n∈ℤ}To show :- A=B∵Let  x∈B  ⇒x = 15m1+12n1…

Q: The sequence {an} satisfies the recurrence relation an = 8an-1+10"-1 and the initial condition a1 =…

A: Given the sequence an satisfy the recurrence relation an=8an−1+10n−1......1 and the initial…

Q: For k e N let l(k) denote the last digit of k when written in its decimal representation. For…

A: Consider the complete graph K2021. Then the vertex set of the graph is V=u1,u2,...,u2021. The weight…

Q: 4) How many distinct symmetric m x m Boolean matrices are there? A symmetric matrix is a matrix for…

A: How many distinct symmetric mm Boolean matrices are there? We will check the answer below: A…

Q: Solve the system: x = y² -y%3D2 %3D у

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Q: R.2. Prove that if A and B – C are disjoint, then AN BCC.

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Q: A third-order homogeneous linear equation and three linearly independent solutions are given below.…

A: Given is a third ordered Homogeneous linear differential equation:y"' + 2y" - y' - 2y = 0 with…

Q: Let X be a compact subset of R and let C(X) denote the set of continuous real-valued functions on X…

A: let X be a compact subset of ℝ and let CX denote the set of continuous real valued functions on X.…

Q: R.2. Using the AM-GM inequality (last proposition in section 4.3), prove that if a and b are…

A: Given : a, b be any two positive real numbers  We have to show using AM-GM inequality that  ab+ba≥2

Q: A given large basket can contain 70 pieces of fruit consisting of apples, bananas, kiwifruit,…

A: