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

f : ℕ₈ → ℕ₈

f(x) = 2x mod 8

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

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

f : ℕ → ℕ x ℕ

f(x) = (x, x)

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"

- Menentukan kebutuhan dan prototipe untuk sistem baru

- Mengevaluasi alternatif dan memprioritaskan kebutuhan

- Memeriksa kebutuhan informasi pengguna akhir dan tingkatkan tujuan system

Pernyataan di atas merupakan proses dalam fase SDLC, di fase manakah itu?

Proof by induction generally requires 3 steps, as outlined below. The first step, while critical, is often assumed in most definitions you come across, but I point it out here for the sake of being thorough.

Let m ∈ ℤ. To prove that P(n) is true for all integers n ≥ m, perform the following steps... 

1. Clearly define the statement you are trying to prove for all n, P(n). It may simply be a verbal statement, like "n is prime," or it may be a mathematical statement that some recursive function definition, f(n), is equivalent to the calculation you're trying to represent recursively.

2. Prove that P(m) is true. This is equivalent to saying "prove P for all minimal elements in the set" if you're dealing with a well-founded set, or "prove the basis case" if you're dealing with a recursive function. 

3. Make an assumption and use it to prove P(n). Assume that n is an is an arbitrary integer n > m, and assume that P(k) is true for all k in the interval m ≤ k < n. Prove that P(n) is true.

Suppose we are going to use this process to prove that every natural number n ≥ 2 is prime or a product of prime numbers. 

1. Let P(n) be the statement, "n is prime or a product of prime numbers" for every natural number n ≥ 2.

What is step 2?

Which of the following relations are partial orders? Select all that apply.