1- Provide the following logical equivalences.(p↔q) ≡( p ∧ q )∧ ( q ∧ p ) (ii) (p∨ q) ≡ ( p ∧ q) ∧ (q ∧ p)2- Test the validity of the following argumentsIf I drop out of school, I'll get a job at the bank. I'm not dropping out of school, so I'm not going to start a job at the bank.(ii) James is a cop or a football player. If he's a cop, he has a gun. James doesn't have a gun, so James is a football player 3- Prove by induction that n3 +2n is divisible by 3 with n > 0.4- Prove that the product of any three consecutive integers is divisible by 6.5- Prove that the sum of the squares of the first n positive integers is 6 n (n + 1) (2n + 1).

The solution for the subparts are given in the following step.

Answered: 1- Provide the following logical…

7th Edition

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Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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1- Provide the following logical equivalences.

(p↔q) ≡( p ∧ q )∧ ( q ∧ p ) (ii) (p∨ q) ≡ ( p ∧ q) ∧ (q ∧ p)

2- Test the validity of the following arguments

If I drop out of school, I'll get a job at the bank. I'm not dropping out of school, so I'm not going to start a job at the bank.
(ii) James is a cop or a football player. If he's a cop, he has a gun. James doesn't have a gun, so James is a football player

3- Prove by induction that n3 +2n is divisible by 3 with n > 0.

4- Prove that the product of any three consecutive integers is divisible by 6.

5- Prove that the sum of the squares of the first n positive integers is 6 n (n + 1) (2n + 1).

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