[24 points] We wish to investigate a new type of relation which we will call Vahidean. A relation R on the set A is Vahidean if: ∀a, b, c ∈ A aRb ∧ aRc → bRc a) Explain, in English, how Transitivity and Vahideanness are different. Give an example of a Vahidean relation on {a, b, c, d} which is not transitive (draw its digraph representation). Give a counterexample that shows your relation is not transitive. b) Is the following an implication of Vahideanness? ∀a, b, c ∈ A aRb ∧ aRc → cRb Explain why or why not. c) Prove that if a relation R is Reflexive and Vahidean then R is an equivalence relation.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

the speed is   miles per hour > is false

step-by-step explanation:

we know that  

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

for the point

substitute the values of x and y

the linear equation is equal to

statements

case a) it takes hours to go miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct

case b) the speed is   miles per hour

the statement is false

because the speed is

case c) the unit rate for the trip is

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took minutes to go the first miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct

the correct answer would be c