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.

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

∵

⇒ 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.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

step-by-step explanation:

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