5) Let R be a binary relation over the positive integers defined as follows: R = {(a, b) | 2b < a < 3b } Determine whether R satisfies the following properties. Give brief justifications for your answers. (i) (ii) (ii) (iv) (v) reflexive irreflexive symmetric anti-symmetric transitive

Let R be the relation, {(a, b) € NxN: a + b² is divisible by 3} Give an example that shows that R is not symmetric. ER and R In each box enter an ordered pair of natural numbers less than 100. Include the parentheses and comma, as you do if you write an ordered pair on paper.

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

Please help me with this question. I don't understand what I did wrong. Please kindly input the correct answer. I've been stuck on this for 1.5 hour now

Please do the following questions with handwritten working out.

Let S be the set of ordered pairs of positive integers, and define (a,b) R (c,d) to mean that 2a-d = 2c-b. Show that R is a transitive relation on S.

Let R be a relation over the positive integers defined as follows: R = {(a,b) | 2b < a < 3b } Determine whether or not R satisfies the following properties. Give a brief justification for each of your answers. (i) reflexive (ii) irreflexive (iii) symmetric (iv) anti-symmetric (v) transitive

Give an example of relation on {1,2,3,4} that is reflexive, not symmetric, and not transitive