If A = {x, y, z}, what is A⁰?

Consider the following partially ordered set (poset):

<S, R>, where...

S = {2, 4, 5, 10} ; R = | (divides)

Which element(s) is(are) the maximal element(s) of S? Select all that apply.

Consider the following partially ordered set (poset):

<S, R>, where...

S = {2, 4, 5, 10} ; R = | (divides)

Which element is the immediate predecessor of 4?

Consider the following partially ordered set (poset):

<S, R>, where...

S = {2, 4, 5, 10} ; R = | (divides)

Which element is the immediate successor of 5?

Is the following function injective, surjective, bijective, or none of these?

f : (0, 1) → ℝ⁺

f(x) = x / (1 - x)

Which of the following statements are true about surjective functions? Select all that apply.

Is the following function injective, surjective, bijective, or none of these?

f : ℕ₈ → ℕ₈

f(x) = 2x mod 8

Let S be the set of three-letter abbreviations for the months of the year. We might define a hash function f: S → {0, 1, …, 11} in the following way:

f(XYZ) = (ord(X) + ord(Y) + ord(Z)) mod 12,

where ord(X) denotes the integer value of the ASCII code for X. (The ASCII values for a-z are 97-122 and A-Z are 65-90)

Compute the value for the key "Jan"

Is the following function injective, surjective, bijective, or none of these?

f : ℕ → ℕ x ℕ

f(x) = (x, x)

True/False: If a function is a bijection, it has an inverse.