Prove: If a² is an even integer, then a is an even integer. [Hint: Assume a² is an even integer and a is odd an odd integer. Derive a contradiction.]

Prove that the difference between two integers is odd if and only if exactly one of the integers is odd.

Let x be an integer. Prove or provide a counterexample: If 4x+7 is odd, then x is odd.

wiev en afslupião of a do ji bowe 2. If the following statement is true, give a proof showing it to be true. If it is false, disprove it by finding a counterexample: Let m and n be positive integers. If 10m |21n, then 10|n.

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.

Give a carefully worded proof for the following statements using direct proof, contrapositive proof or proof by contradiction. No matter which proof method you choose to use, make sure you follow the outline properly. (If-and-Only-If Proof) Given an integer a and b, then b2(a + 3) is even if and only if a is odd or b is even. (Use the basic definitions of even and odd in your proof.)

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

The world’s largest sign for Coca­Cola is located in Arica, Chile. The rectangular sign has a length of 400 feet and an area of 52,400 square feet. Find the width of the sign.

Let                                 Numbers are all single digit. A =  3 4     1 2  and B =  4 3     2 1 . (a) Compute AB. AB =                             (b) Compute BA. BA =

If a and b are odd positive integers, and the sum of the integers, less than a and greater than b, is 1000; then find a and b.