R on the set {1,2,3,4,5}, so that (x,y) is in R if 3 divides x+y. List the elements of R.

Mathematics

1 answer:

ANTONII [103]3 years ago

7 0

Answer: The elements of R are

R = {(1, 2), (1, 5), (2, 1), (2, 4), (3, 3), (4, 2), (4, 5), (5, 1), (5, 4)}.

Step-by-step explanation: We are given a relation R on the set {1, 2, 3, 4, 5} so that (x, y) is in R if 3 divides x+y.

We are to list the elements of R.

We see that

if x = 1 and y = 2, 5, then x + y = 3 and 6 so that 3 divides x+y.

If x = 2 and y = 1, 4, then x + y = 3 and 6 so that 3 divides x+y.

If x = 3 and y = 3, the x + y = 6 so that 3 divides x+y.

If x = 4 and y = 2, 5, then x + y = 6 and 9 so that 3 divides x+y.

If x = 5 and y = 1, 4, then x + y = 6 and 9 so that 3 divides x+y.

Therefore, the elements in R are listed as follows :

R = {(1, 2), (1, 5), (2, 1), (2, 4), (3, 3), (4, 2), (4, 5), (5, 1), (5, 4)}.

Thus, R = {(1, 2), (1, 5), (2, 1), (2, 4), (3, 3), (4, 2), (4, 5), (5, 1), (5, 4)}.

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A. Plot the data for the functions f(x) and g(x) on a grid and connect the points.

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a) see the plots below

b) f(x) is exponential; g(x) is linear (see below for explanation)

c) the function values are never equal

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a) a graph of the two function values is attached

b) Adjacent values of f(x) have a common ratio of 3, so f(x) is exponential (with a base of 3). Adjacent values of g(x) have a common difference of 2, so g(x) is linear (with a slope of 2).

c) At x ≥ 1, the slope of f(x) is greater than the slope of g(x), and the value of f(x) is greater than the value of g(x), so the curves can never cross for x > 1. Similarly, for x ≤ 0, the slope of f(x) is less than the slope of g(x). Once again, f(0) is greater than g(0), so the curves can never cross.

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