4023f11ps1

4023f11ps1 - X is a subset of A £ B , then X need not be...

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Homework #1 Due: August 29, 2011 1. Let A = f a; b; c; d; e g , B = f 1 ; a; b; 2 ; c g , and C = f 3 ; c; a; 1 ; f g . Answer the following questions concerning these sets. Remember that the cardinality of a set S , denoted j S j , means the number of elements in the set. Also the relative difierence of sets S and T , denoted S ¡ T , is S ¡ T = f x 2 S : s = 2 T g : That is, S ¡ T consists of all of the element of S that are not elements of T . (a) Write the set A \ B . (b) Write the set A [ B . (c) Write the set A ¡ ( B \ C ). (d) Write the set ( A \ C ) £ ( C n B ). (e) What is the cardinality of P ( A )? Remember that P ( A ) denotes the power set of A . (f) What is the cardinality of A £ C ? (g) Which set has more elements: P ( A £ C ) or P ( A ) £ P ( C )? 2. Give an example to show that if
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Unformatted text preview: X is a subset of A £ B , then X need not be of the form C £ D where C is a subset of A and D is a subset of B . 3. How many functions are there from a set X with 5 elements to a set Y with 7 elements? How many of these functions are injective? 4. Determine if each of the following statements is true or false. (a) 40 · 13 mod 9 (b) ¡ 29 · 1 mod 7 (c) ¡ 29 · 6 mod 7 (d) 132 · 0 mod 11 5. Exercise 10, Page 10 from Nagpaul-Jain. 6. Exercise 11, Page 10 from Nagpaul-Jain. Add to this exercise: Write the equivalence class of (5 ; 3). Math 4023 1...
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This document was uploaded on 12/28/2011.

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