Discrete Mathematics Answers

Draw the Hasse diagram foe 2,3,4,5,10,12,25,30?

Find the Cartesian product A × B × C where A = (0, 1), B = (1, 2) and C= (0, 1, 2)

Solve the recurrence relation of an=3an-3an-2-an-3 n>=3 a0=1 a1=-2 a2=-1

Let 𝑈 = {𝑎, 𝑒, 𝑖, 𝑜, 𝑢, 3, 6, 9, 12}, 𝐴 = {𝑜, 𝑢, 3, 12}, 𝐵 = {𝑢, 9, 6, 𝑎}, 𝑎𝑛𝑑 𝐶 = {𝑢, 12, 𝑖, 𝑜}.

1. Find 𝐶 ∪ 𝐴

2. Find (𝐶′ ∩ 𝐵) ∪ 𝐶

3. Find {(𝐵′ ∪ 𝐴)′ − 𝐴 ∪ (𝐵 ∩ 𝐵′)}

Make a truth table to determine the logical equivalence of the statements.

1. ~ P → Q ↔ P ∨ Q
2. ~ (P → Q) ↔ P ∨ ~Q.

Prove that a real number 𝑥 is irrational if and only if 5𝑥 is irrational

Find out if the following functions are one-to-one and/or onto. a. 𝑓: 𝑍 → 𝑅, 𝑓(𝑥) = 𝑥 3 + 1 b. 𝑓: 𝑅 + → 𝑅 +, 𝑓(𝑥) = |𝑥| + 5

Let  . P(x): x²/2 = x

Find the following then identify their truth values.

1. P (1)
2. P (2)
3. ꓯn, P(n)
4. ⱻn, P(n)

4. For each of these pairs of sets, determine whether the first is a subset of the second, the second is a subset of the first, or neither is a subset of the other. a) the set of people who speak English, the set of people who speak English with an Australian accent b) the set of fruits, the set of citrus fruits c) the set of students studying discrete mathematics, the set of students studying data structures

What is the probability that when a coin is flipped six times in a row, it lands heads up every time?