1.

How many non-zero entries does the matrix representing the relation R on A = {1, 2, 3, , 20} consisting of the first 20 positive integers have if R is {(a,b) | b > 3*a}?

Select one:

a. 51

b. 102

c. 57

d. 400

2.

Which of the followings is a solution to the recurrence relation a_n = 10*a_n-1 25*a_n-2 with the initial conditions a₀ = 2 and a₁ = 5?

Select one:

a. a_n = 2*5ⁿ n*5ⁿ

b. a_n = 2*5ⁿ n²*5ⁿ

c. a_n = 2*(5)ⁿ 3*n²*(5)ⁿ

d. a_n = 2*(5)ⁿ 3*n*(5)ⁿ

3.

Let R be the relation on the set {1, 2, 3, 4} containing the ordered pairs (1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4). Find R².

Select one:

a. R²={(1, 1), (1, 4),(2, 1),(2, 4), (3, 3), (3, 4)}

b. R²={(1, 1), (1, 4),(2, 1), (2, 2), (2, 4), (3, 3), (3, 4)}

c. R²={(1, 1), (1, 4),(2, 1),(2, 4), (3, 4)}

d. R²={(1, 1), (1, 4),(2, 1),(2, 4), (3, 3), (3, 4), (4, 1)}