# lec0207 - CS 173 Discrete Mathematical Structures Cinda...

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CS 173: Discrete Mathematical Structures Cinda Heeren [email protected] Rm 2213 Siebel Center Office Hours: W 9:30-11:30a

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Cs173 - Spring 2004 CS 173 Announcements Homework 4 available. Due 02/12, 8a. Midterm 1: 2/23/06, 7-9p, location SC 1404.
CS 173 Functions - misc. properties f( ) = f({a}) = {f(a)} f(A U B) = f(A) U f(B) f(A B) f(A) f(B) Michael Tito Janet Cindy Bobby Katherine Scruse Carol Brady Mother Teresa

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Cs173 - Spring 2004 CS 173 Functions - misc. properties f(A B) f(A) f(B)? B) = {x : 5 a (A B), f(a) = x} Choose an arbitrary b B), and show that it must also be an element of f(A) f(B). So, 5 B) such that f(a) = b. If a A (it is), then f(a) = b f(A). If a B (it is), then f(a) = b b f(A), and b f(B), so b
CS 173 Functions - misc. properties f -1 ( ) = f (A U B) = f (A) U f (B) f (A B) = f (A) f Michael Tito Janet Cindy Bobby Katherine Scruse Carol Brady Mother Teresa

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CS 173 Functions - injection A function f: A B is one-to-one (injective, an injection) if 2200 a,b,c, (f(a) = b f(c) = b) a = c Every b B has at most 1 preimage. Michael Tito Janet Cindy Bobby Katherine Scruse Carol Brady Mother Teresa
CS 173 Functions - surjection A function f: A B is onto (surjective, a surjection) if 2200 b B, 5 a A f(a) = b Not onto Every b B has at least 1 preimage. Michael Tito Janet Cindy Bobby Katherine Scruse Carol Brady Mother Teresa

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Cs173 - Spring 2004 CS 173 Functions - bijection A function f: A B is bijective if it is one-to-one and onto. Isaak Bri Lynette Aidan Evan Every b B has exactly 1 preimage. An important implication of this characteristic: The preimage (f -1 ) is a function! Cinda Dee Deb Katrina Dawn
Cs173 - Spring 2004 CS 173 Functions - examples Suppose f: R + R + , f(x) = x 2 .

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lec0207 - CS 173 Discrete Mathematical Structures Cinda...

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