Please do the question 5 and 6. I dont\\\'t want a short answer or just one ques

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Please do the question 5 and 6. I dont't want a short answer or just one question's answer, I need them all. Only when you give me the answers of questions 5 and 6 with detail, then I will give you the points.

Use induction on n to prove the general inclusion-exclusion principle: Let n be a positive integer and A1, A2,..An be finite sets. For any subset / = {i1,i2, ik} Nn. let At denote the intersection Problem 2: Let n be a positive integer and let A C N2n satisfy |.4| = n+1. Prove that there exist distinct elements a1,a2epsilon A such that a1 divides a2. (Hint: Think about the Pigeonhole Principle and a function / defined by the rule that f(a) is the greatest odd integer which divides a.) Problem 3: Prove that a finite non-empty set of real numbers contains a minimum element. Problem 4: Let .4 and B be finite sets of real numbers with .4 C B. Prove that min B

Explanation / Answer

Please find complete solution in this PDF... And please rate my hard work

https://dl.dropboxusercontent.com/u/20327748/3000%20dream.pdf

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