Question

Let A = {2, 4} and B = {1, 3, 5} and define a relation U, V and W from A to B as follows: For every (x, y) is in A ✕ B,every (x, y) is in U means thay y - x > 2. every (x, y) is in V means thay y - 1 = x/2. W = {(2, 5), (4, 1), (2, 3)}. (a) Draw arrow diagrams for U, V and W (b) Indicate whether any of the relations U, V, and W are functions.

Answer 1

Answer:

Given,

A = {2,4},

B = {1, 3, 5}

U, V and W are the relation from A and B as follow,

U = { (x,y) : y - x > 2, x∈A, y∈B }

V = { (x,y) : y - 1 = x/2, x∈A, y∈B }

W = {(2, 5), (4, 1), (2, 3)},

∵ 1-2 = -1, 1-4 = -3, 3-2 = 1, 3-4 = -1, 5-2 = 3, 5 - 4 =1,

Thus, U = { (2,5) },

Also, 1 - 1 = 0, 3 - 1 = 2, 5 - 1 = 4

∵ $2=\frac{4}{2}\text{ where }4\in A$

⇒ V = { (4,3) }

(a) Drawing is shown below,

(b) Since, a relation is called function if each input has only one output,

Hence, U and V are functions while W is not the function.