homework7 - LOGIC AND PROOF HOMEWORK 7 1. 4.1.5 (part b) 2....

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Unformatted text preview: LOGIC AND PROOF HOMEWORK 7 1. 4.1.5 (part b) 2. The characteristic function of a set A in a universe U is defined to be 1 if xA x 0 if x A Use this definition to complete exercise 4.1.7. 3. 4.1.16 (part b) 4. Let f: A B and let D be a subset of A. We say that the restriction of f to D is the function f |D = { (x, y): y = f(x) and x D} Prove that if f is a function from A to B, then the restriction is a function from C to B. 5. Prove that if f is an increasing function on an interval I, and g(x) = ‐f(x) for all x I, then g is a decreasing function. 6. Prove that the function f: \{‐1} defined by f x is 1‐1 but not onto. x 4 5. Calculate the largest codomain 7. Consider the function f: + defined by f x such that f is onto. 8. Prove that any linear function f: defined by f(x) = mx + b is a bijection. ...
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This note was uploaded on 09/22/2011 for the course MAC 2311 taught by Professor Evinson during the Spring '08 term at University of Central Florida.

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