Math 131a midterm

Math 131a midterm - Math 131a Midterm 1 Lecture 2 Spring...

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Unformatted text preview: Math 131a Midterm 1 Lecture 2 Spring 2009 Name: Instructions: There are 4 problems. Make sure you are not missing any pages. Unless stated otherwise (or unless it trivializes the problem), you may use without proof anything proven in the sections of the book covered by this test (excluding the exercises). Give complete, convincing, and clear answers (or points will be deducted). No calculators, books, or notes are allowed. Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. Question Points Score 1 10 2 10 3 10 4 10 Total: 40 1. (10 points) Suppose that f : C D is an injective function, and that A,B C. Prove that f ( A B ) = f ( A ) f ( B ) . (Here f ( A ) = { f ( x ) : x A } and similarly for B and A B .) Solution: First, we show f ( A B ) f ( A ) f ( B ) . Suppose that y f ( A B ) . Then by definition, there is an x A B with f ( x ) = y. Since x A, we then have y f...
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This note was uploaded on 12/05/2009 for the course MATH 262447221 taught by Professor Weisbart during the Spring '09 term at UCLA.

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Math 131a midterm - Math 131a Midterm 1 Lecture 2 Spring...

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