PLEAS HELPP MEEE:< RELATIONS AND FUNCTIONS
A. Let A = {2, 3, 4} and B = {6, 8, 10} and define a relation R from A to B as follows: For all (x, y) ∈ A x B,
(x, y) ∈ R means that yx is an integer.
a. State explicitly which ordered pairs are in A x B and which are in R.
b. Is 4 R 6? Is 4 R 8? Is 3 R 8? Is 2 R 10?
c. What are the domain and co-domain of R?
Solution:

B. Let E = {1, 2, 3} and F = {-2, -1, 0} and define a relation R from E to F as follows: For all (x, y) ∈ E x F,
(x, y) ∈ R means that x - y3 is an integer.
a. Which set of ordered pairs are in R.
b. Is 3 R 0? Is 1 R (-1)? Is 2 R (-1)? Is (3, -2) ∈ R?
c. What are the domain and co-domain of R?
Solution:

C. Let X = {2, 4, 5} and Y = {1, 2, 4, 6}. Which of the following determine functions from X to Y?

1. {(2, 6), (2, 2), (1, 1), (5, 4)}


2. {(2, 4), (4, 1)}


3. {(2, 4), (4, 1), (4, 2), (5, 6)}


4. {(2, 6), (4, 2), (5, 2)}


5. {(4, 2), (5, 4)}
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Determine if the following statement is true or false. the normal curve is symmetric about its​ mean, mu. choose the best answer below. a. the statement is false. the normal curve is not symmetric about its​ mean, because the mean is the balancing point of the graph of the distribution. the median is the point where​ 50% of the area under the distribution is to the left and​ 50% to the right.​ therefore, the normal curve could only be symmetric about its​ median, not about its mean. b. the statement is true. the normal curve is a symmetric distribution with one​ peak, which means the​ mean, median, and mode are all equal.​ therefore, the normal curve is symmetric about the​ mean, mu. c. the statement is false. the mean is the balancing point for the graph of a​ distribution, and​ therefore, it is impossible for any distribution to be symmetric about the mean. d. the statement is true. the mean is the balancing point for the graph of a​ distribution, and​ therefore, all distributions are symmetric about the mean.