Prove the following statement by contradiction. For any integer n, if n² + 4n + 5 is even, then n is odd. What would be assumed to be true? On? + 4n + 5 is odd and n is even On? + 4n + 5 is even On + 4n + 5 is odd and n is even On? + 4n + 5 is even and n is even On + 4n + 5 is even and n is odd On? + 4n + 5 is odd

By dragging statements from the left column to the right column below, construct a valide proof of the statement: For all integers n, if 13n is even, then n is even. The correct proof will use 3 of the statements below. Statements to choose from: Let n be an arbitrary integer and assume n is odd. Let n be an arbitrary integer and assume n is even. Since 13 is odd and the product of an odd number and an even number is even, Let n be an arbitrary integer and assume 13n is even. 13n must be even Since 13 is odd and the product of odd numbers is odd, 13n must be odd. n must be even Since an even number divided by 13 must be even, Your Proof: Put chosen statements in order in this column and press the Submit Answers button.

Which one of the following expressions is the value of the cosine of the acute angle between the vectors u = (1,2, 3) and v = (1, –2,3)? 3 (A) 7V2 2 (B) 7 (C) 7/2 3 (D)

For each of the statements below (which all happen to be false), look atthe “proofs” that have been provided and explain in one or two sentences what error has been made by the author.

In each of the following statements, n represents a positive integer. One of the statements is true and the other two are false.  If n is even, then n is not prime  if n is a square number, then n is not prime  if n is a prime number and n ≥ 10, then n+2 is prime or n+4 is prime.  A. What two statements are false and in each case give a counter example to show that it is false  B. Prove the true statement

(3) Use a proof by contrapositive to prove the following statement: If 6n² + 5n+7 is odd, then n is even.

Prove the following statements: (a) If n is a positive integer then n 2 + 1 is an odd positive integer. (b) If n 2 + 1 is an even positive integer, and n is a positive integer then n is an odd positive integer.

Pls. answer these two questions by typing and not by handrwriting

Evaluate as in is there a mistake in the proof? If so show. If no mistake state result or show.