3330_Final_Practice_Sol

3330_Final_Practice_Sol - Math 3330 Spring 2010 Final...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
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?
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 2
3. Proof by induction: Prove that 5 is a factor of 72 nn for all positive integers n.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 4
5. Let { } 10 [0],[2],[4],[6],[8] H = ] with the operation of multiplication modulo 10. Prove or
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 9

3330_Final_Practice_Sol - Math 3330 Spring 2010 Final...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online