Discrete Mathematics Answers

Use the truth tables method to determine whether (¬p ∨ q) ∧ (q → ¬r ∧ ¬p) ∧ (p ∧ r) is

satisfiable.

(P^Q^R)V (¬P^Q^R)V(¬P^¬Q^¬R)

Use the Principle of Mathematical Induction to prove that (2𝑛)! /(2ⁿ)𝑛! is odd for all positive integers.

Given the following 2 premises, 1. 𝑝 → (𝑞 ∨ 𝑟) 2. 𝑞 → 𝑠 Prove 𝑝 → (𝑟 ∨ 𝑠) is valid using the Proof by Contradiction method. 

F. How many different sequences, each of length r, can be formed using elements

from A if

(a) elements in the sequence may be repeated?

(b) all elements in the sequence must be distinct?

Show that the following logical equivalences hold for the

Peirce arrow ↓, where P ↓ Q ≡ ∼(P ∨ Q).

a. ∼P ≡ P ↓ P

b. P ∨ Q ≡ (P ↓ Q) ↓ (P ↓ Q)

c. P ∧ Q ≡ (P ↓ P) ↓ (Q ↓ Q)

H d. Write P → Q using Peirce arrows only.

e. Write P ↔ Q using Peirce arrows only.

F. Define and give examples of injective surjective and bijective functions. Check the injectivity and surjectivity of the following function f: NN given by f(x)=x2

Prove that the relation R:{(x,y)|x-y is divisible by 3} is an Equivalence relation.(R is

defined over Z) L2 CO2 10

What and Define crashing of networks in mathematical of foundations of computer science