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# Discrete Math- Final Homework

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1

Given S={0,1,2,3,4,5}, find the partition induced by the equivalence relation R where R={(0,0),(0,4),(1,1),(1,3),(4,5),(0,5),(5,4),(5,0),(5,5),(2,2),(3,1),(3,3),(4,0),(4,4)}. Explain.

2

Let A and B be any sets. Prove the following set identity using the laws of set theory (set identities). Justify each step with the law you used. Missing steps and missing justification will be penalized. (1 point)

A ∩(B ∪A’) ∩B’ = Ø

3

Let the relation R = {(0,0), (0,3), (1,0), (1,2), (2,0), (3,2)}

Find R’ the transitive closure of R. (1 point)

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