Discrete Math Problem 1 What is wrong with this proof? Theorem 1. 3 is greater t

Question

Discrete Math

Problem 1 What is wrong with this proof? Theorem 1. 3 is greater than 5. Proof Every integer number is either less than 5 or greater than 5 or equal to 5. Let c be an arbitrary integer number. Therefore, it is less than 5 or greater than 5 or equal to 5. Suppose it is greater than 5. By the rule of universal generalization, if an arbitrary number is greater than 5, every number is greater than 5. Therefore, 3 is greater than 5. Problem 2 Give a direct proof that, for all integers k and e, if k and l are both even, then k +l is even. Problem 3 Give a proof by contraposition that, for all integers k and 1, if is odd, then k and & are both odd. Problem 4 Prove that V4 is irrational. Hint: Please, imitate the proof of "V2 is irrational Problem 5 Give a proof by contradiction that, for any integer n, if n2 -1 is odd, then n is even.

Explanation / Answer

Please post all the problems separatey as per chegg rules.

1.

3 is not an arbitrary number. 3 is a specific number.

E.g. if I choose 7, it is not greater than 5.

Also the paragraph doesn't prove that any arbitrary number is greater than 5.

2.

any even number would be of the form = 2p

so let k = 2n

l = 2m

where m and n are also integers.

so k+l = 2m + 2n = 2(m+n)

m+n is integer so 2(m+n) is even.

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