(b) Prove that for every n e Z, n³ +n is even. (c) Prove that for all ne Z, n is odd if and only if n + 2 is odd. (d) Prove that the product of two consecutive integers is even.

Q: Prove that (-1ti3)" + (-1-is3)" has either the value 2n+' or the value -2" if r is any ). integer…

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Q: (2-c) Critically evaluate all techniques used in parts 2-a and 2-b, commenting on their…

A: Errors can result prior to computation in the form of measurement errors or assumptions in modeling.…

Q: Compute A - 613 and (613)A, where A = - A-613 = ☐ 6 - 4 3 2 -7 - 3 1 3

A:

Q: 16 M = 7 -5 Find formulas for the entries of M", where n is a positive integer. M" =

A: We have to find the entries of matrix Mn.

Q: Is it possible to raise a positive number b to a power and obtain a negative number? Is it possible…

A: The given statement is " The possibility to raise a positive number b to a power and obtain a…

Q: Show by contraposition that : Vx ERx?-7x-820 - x2 8 or x S-1

A: In this method, we prove negation of antecedent and get contradicted and get our required results.

Q: I-11 Evaluate the following integral dr. (z² + 9)(z + 2) Maximum number of characters (including…

A:

Q: Compute ATBT and BT AT by hand if possible. If not possible, describe why. A = 2 3 −1 0 B = 10 -1 0…

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Q: Show that An, n > 5 is simple.

A: Sol:- To show that An, the alternating group of even permutations of degree n, is simple for n ≥ 5,…

Q: 8) 58(x-1) = 6252x-2

A: 58(x-1)=625(2x-2)

Q: How many 10 digit real even number can be created (It cannot start with a 0) with 5 zeroes and 5…

A: Basic concepts of making combination are used. Information given, As we have only two choices of…

Q: Prove that 1+1=2

A: To prove: 1 + 1 = 2

Q: Prove that there is a positive number z so that z^5 + 10z = 10.

A: TO PROVE:-  There is a positive number z satisfying z5+10z=10 GIVEN :- z5+10z=10

Q: Compute each of the following. (2bdm from 5.4) a) (12) (1253) b) (1423) (34) (56)(1324) c) (12)-¹

A:

Q: 9 – i 3 + 9i If A = find A*. 7+ 5i -4 + 8i ( ) ? ? ? ? A*

A:

Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: form of (3+3i)^5

A: Given,      (3+3i)5

Q: A product engineer wants to optimize the cutting of strips of wood, which are used to ma plywood. To…

A: 1. Null Hypothesis: H0: There is no significant difference in the mean of torque force for log…

Q: 4 -7 -3 -2 8. Let A = [^, and 8 = [ -21. Compute A-1B. -1 2 1

A: first we compute A^-1 by using formula

Q: Show that 2 + V5 is imational number

A:

Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

Q: what are the first three terms in the binamial, expansion of (2a-0,5b) 1.

A: Given

Q: Prove that m^3 + 2n^2 =36 has no solution in positive integers.

A: Prove that  there is no solution for positive integers.Let if for for

Q: Find the number of positive integers not exceeding 100 that are either odd or the square of an…

A: The objective is to find the number of positive integers not exceeding that are either odd or the…

Q: 28000 +38000 + 48000 + 58000 + 68000 Prove that 1 8000 is a multiple of 13 using Fermat's Little…

A: Given that                                 we have to prove that it is multiple of 13 by using…

Q: Compute A -213 and (213)A, where A = A-213= 5 - 4 -4 -1 2 3 - 5 1 3

A: In this question, we will compute the matrix.

Q: 27. Show that if x and y are positive real numbers that have the same first n digits in their…

A:

Q: How do we know that -1 and -2 will be in the field?

A: Given F is field, So,  0, 1∈F ( since a field F must contain zero element and unity ) A field is…

Q: Let Find formulas for the entries of M", where n is a positive integer. Hint: a formula such as 5…

A: The given problem is to find the entries of Mn for the given following matrix M. We have to find the…

Q: 3. Show that (5+ 13)e + (5- i3)-" is a real number if is also a real number.

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Q: If A= xe Z:2" = 1 and B = {x e Z:-4 < 3x-1<11}, then find n(A×B),where Z is a set of integers.

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Q: Find the value of (1+ i)148 – (1 – i)'48 Do not just state the answer. Show your computations.

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Q: A product engineer wants to optimize the cutting of strips of wood, which are used to make plywood.…

A: As per the multiple questions rule, we are allowed to solve first question at a time. Kindly repost…

Q: Using strong PMI, show that every natural number is a sum of powers of 2. For example, 11 = 23 +2¹…

A: Using strong PMI, we have to show show that every natural number is a sum of powers of 2.

Q: Did not get this problem right

A: Rewriting the expression: Simplifying:

Q: [₁23], decode the following message: Message: -1, 4, 30, -41, 39, -58, 22, -33, 31, -46, 23, -34, 1,…

A: