Answer:
a) r ^ ¬q
b) p ^ꓥqꓥ^ r
c) r → p
d) p ^ ¬qꓥ^ r
e) (p ^ q) → r
f) r ↔ (q v p)
Step-by-step explanation:
ꓥ^ = AND Conjunction
vꓦ = OR disjunction
¬ = NOT Negation
↔ = Double Implication
→ = implication
Answer:

Step-by-step explanation:
A line is a one-dimensional figure that has no thickness and extends infinitely in both directions.
A line segment is a line that has two end-points and a ray is a line that has one end-point.
Given equation is 
To find : a line that lies entirely in the set defined by the given equation.
Solution:
Take 
Check:

Therefore,
satisfy the given equation.
Answer: Straight piecework plan
Step-by-step explanation:
The Straight piecework plan is a type of incentive system in which the rate per unit output is constant and fixed at a specific value. And the total earnings of a worker is calculated by multiplying the value of its total output by the rate per unit output.
In the case above the rate per unit invoice processed is fixed, so employees are paid based on the number of invoice processed per hour which makes it a Straight piecework plan system.
By definition, the average rate of change is given by:

We evaluate each of the functions in the given interval.
We have then:
For f (x) = x ^ 2 + 3x:
Evaluating for x = -2:

Evaluating for x = 3:

Then, the AVR is:




For f (x) = 3x - 8:
Evaluating for x =4:

Evaluating for x = 5:

Then, the AVR is:



For f (x) = x ^ 2 - 2x:
Evaluating for x = -3:

Evaluating for x = 4:

Then, the AVR is:




For f (x) = x ^ 2 - 5:
Evaluating for x = -1:

Evaluating for x = 1:

Then, the AVR is:




Answer:
from the greatest to the least value based on the average rate of change in the specified interval:
f(x) = x^2 + 3x interval: [-2, 3]
f(x) = 3x - 8 interval: [4, 5]
f(x) = x^2 - 5 interval: [-1, 1]
f(x) = x^2 - 2x interval: [-3, 4]