Describe the following sets in terms of graphs, supergraphs, and subgraphs of functions appropriate: A = {(x, y, z) | y2 + x < yz ≤ x + y2 + z2}B = {(x, y, z,w) | x + w2 < y + z3 ≤ x + z2 + w3)}C = {(x, y) | | y2 − y |≤ x, | y + 2 |≤ 1} Please give the answers step by step as explicitly as possible. thank you

A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.