3330_Final_Practice_Sol

# 3330_Final_Practice_Sol - Math 3330 Spring 2010 Final...

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Math 3330 Spring 2010 Final Reivew Practice Problems 1. Let A be a nonempty set and let be the power set of A (the set of all subsets of A). Define the operation " " on the set as normal set intersection. Explain your reasons for the answers to each of the following questions. () PA ( ) (a). Is the system closed? (b). Is the operation " " commutative? (c). Is the operation " " associative? (d). Does the set have an identity element for the operation " "? (e). Which elements in have inverses for this operation?

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2. Define a relation R on the set of rational numbers by, for all rational numbers x and y, xRy if and only if x-y is an integer. Prove or disprove that R is an equivalence relation.
3. Proof by induction: Prove that 5 is a factor of 72 nn for all positive integers n.

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4. Random proofs: (a). Given a multiplicative group G, prove that the inverse of an element is unique (b). Suppose and and (, | ac | bc ) 1 ab = . Prove or disprove that . | ab c (c). Let 0 be the additive identity of a ring. Prove that 0*x=0 for all x in the ring.
5. Let { } 10 [0],[2],[4],[6],[8] H = ] with the operation of multiplication modulo 10. Prove or

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## This note was uploaded on 08/10/2011 for the course MATH 3330 taught by Professor Flagg during the Spring '11 term at University of Houston.

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3330_Final_Practice_Sol - Math 3330 Spring 2010 Final...

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