Prove the correctness or give a counterexample for the following statement. You must state whether the statement is true or false and then show your arguments. (“->” means “implies”). a.Knot -> Deadlock

Write the negation of each of the following statements (hint: you may have to apply DeMorgan's Law multiple times) (a) ~ p^~ q (b) (p^q) → r

Below are some statements; the domain of each is the set of all integers. For symbolic statements, thenegation symbol (¬) must not apear in your answer. For English statements, don’t use “It is not the casethat” or just the word “not” to form the negation.For each one, state whether the statement is TRUE, FALSE, or CAN’T BE DETERMINED. For all that onesthat are TRUE or FALSE, state the negation:1.∃n(nis even)2.∀a∀b(3a≥2b)3.∀a∃b(ab= 1)

write a contrapositive proof

PS: Please complete all of the subparts as they are all the same question and not in Handwritten paper.

(Pythagorean Triples) A right triangle can have sides that are all integers. The set of threeinteger values for the sides of a right triangle is called a Pythagorean triple. These three sides mustsatisfy the relationship that the sum of the squares of two of the sides is equal to the square of thehypotenuse. Find all Pythagorean triples for side1, side2, and the hypotenuse all no larger than 500.Use a triple-nested for loop that simply tries all possibilities. This is an example of “brute-force”computing. It’s not aesthetically pleasing to many people. But there are many reasons why thesetechniques are important. First, with computing power increasing at such a phenomenal pace, solutions that would have taken years or even centuries of computer time to produce with the technology of just a few years ago can now be produced in hours, minutes or even seconds. Recentmicroprocessor chips can process a billion instructions per second! Second, as you’ll learn in moreadvanced computer science…