(3) 5. Write a direct proof to show that if m is an even integer then Sm+ 3 is an odd integer. (3)6. Write an indirect proof to show if 3m +1 is an odd integer then m is an even integer

Q: Consider nonnegative integer solutions of the equation xi + x2 + x3 + x4 + x5 + æ6 = 30.

A: The non-negative integer equation is x1+x2+x3+x4+x5+x6=30Since ,xi-number varying from 0 to…

Q: You are given a real number N. How should you write it as a sum of two real numbers so that their…

A:

Q: In(2x² – 2) = In- 2x2 = 2 In x 2. True False

A: Check whether ln2x2-2=ln2x22=2lnx is true or false as follows. Recall, ln(a)-ln(b)=lnablnxa=alnx

Q: Express as a polynomial.

A: Here given as 4z4-3z2+1-zz3+4z2-4

Q: Show that (k^2 * (k+1)^2)/(4) + (k+1)^3 is equal to ((k+1)(k+2)/2)^2

A:

Q: -2{-12/-3+2[2²-12-√100]-(3²)}

A: We want to solve the given basic mathematical operation problem.

Q: Find each (n+3)(n+2) (4n 5)(3n + 2) (n+7)(n + 5)

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: The positive integer 2011 2012 2013 . . . 2022 2023 has 52 digits. Without changing the order of any…

A:

Q: I am thinking of a three-digit number. All the digits is odd, the ten's digit is a perfect square,…

A:

Q: Evaluate ak+2 if ap

A:

Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

Q: Prove that for a positive integer n we have that 33n+3 – 26n – 27 is divisible by 169. - -

A: The given expression is: 33n+3-26n-27 This is to be proved that the expression is divisible by 169.

Q: Find a counterexample to show that each of the statements is false.

A:

Q: Select two expressions equivalent to 15a² – 5a - 11 (Select all that apply.) (14a² − 9a +1)+(a² + 4a…

A: Given; 15a2-5a-11.

Q: Which of the following is NOT correct ? 3x (6+9)=3x6+3x9 is distributive 3x (6+9)= (6+9) x 3 is…

A:

Q: Can someone explain how (n + 1) and (n + 2) can be integers? and also how can they be bigger than 1?

A: Answer: 1:  The solution is as given below:

Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

A:

Q: 6. Simplify these algebraic expressions. a) 2m + 12n - 3m - Op+ 10p +m – n- 12p b) 5r+ 13t +…

A:

Q: 1. Can you reduce this expression?  (x2 + 3x)/ (2x - 1) 2. Aren't there math symbols available on…

A:

Q: Prove that 3x3+ 5x - 11 has a root between x=1 and x=2. Thanks!

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: If X is the smallest, or first of three consecutive even integers express the sum of all three…

A:

Q: 3 Solve х — 1 x + 4 ||

A: given,        3x-1=2x+4

Q: Show that n-lis divisible by 8, if n is an odd positive integer

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.