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Material Type: Exam; Class: Discrete Structures; Subject: Computer Science; University: Northeastern Illinois University; Term: Spring 2001;
Typology: Exams
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CS 201-31, Discrete Structures, Spring 2001, Assignment 3 Solution Section 2.1, page 70:
Section 2.7, page 96: Prove the following statement: If x is odd, then x^2 is odd. Proof: (1) Assume x is odd.
Section 2.2, page 73:
Proof:
(2) B is finite means we can write B in list format without ellipses.
(4) This means that A can be written in list format without ellipses—simply take the representation of set B in step (2), and cross out any elements in B that are not in A. (5) Thus A is finite. PROOF COMPLETE. 6b) Is every subset of an infinite set infinite? This question translates to determining whether the following statement is True or False:
We prove this is FALSE. An if-then is false exactly when the premise is TRUE and the conclusion is FALSE. A counterexample suffices: Let B be the natural numbers and let A be the set {1,2,3}. Section 2.4, pages 81, 82: