Let R = (6, 5). Calculate the length of OR. ||OR||

pints)Let f(x) = x² and g(x) = |x|. Determine f(2), f(3), and f(5). b) Determine g(-4), g(10), and g(6). Use part a) to show that f(2 + 3) = f(2) + f(3) is not a true statement. use part b) to show that g(-4+10) = g(-4) + g(10) is not a true statement.

Let A = {1, 2} and B = {-1,0, 1}. Answer the following questions using careful, accurate notation for each: (a) A x B = (Do not type any space or unnecessary characters.) (b) Write two non-empty relations from A to B: (Separate your relations with a semicolon.) (c) How many relations from A to B are there in total? (d) Write a function from B to A in set notation: (e) Is the relation R = {(x, y) | x E A, y E B, x y} a function from A to B? • Justify your answer by providing a short reason here: ere to search

Determine whether the statement is true or false. Prove the statement if it is true, and give a counterexample if it is false. (i) For all real numbers x and y, [x – y] = [x] – [y]. (ii) Let a, b and c be integers. If a|(bc), then a|b or a|c. (iii) Let m and n be integers. If m is even and n is odd, then m² – n² is odd.