# sampleex01 - /14/2006 SE3306 Mathematical Foundations of SE...

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Unformatted text preview: Exam 01 02/14/2006 SE3306 Mathematical Foundations of SE Name: WebCT ID: Instructions: Read through the whole exam ﬁrst and plan your time. The exam is worth 25 points, with each question valued as indicated. Closed book: Reference to notes, the text or other material is not permitted. Time: You have one hour and ﬁfteen minutes to complete all questions. Write all your answers on this paper. 1 when both and are false? Question 2 (2 points) What is the converse and contrapositive of the statement “If it is sunny, then I will go swimming”? 2 ¥ ¡ §¥ ¦  ¡ © §¥ ¨¦¤¢ £ ¡ Question 1 (2 points) What is the truth value of 1. using a truth table. 2. using logical equivalences 3  .” What are the truth values of § ¢  ¡¢ ¢ ©§¥¢ ¨¦ ¤ Question 4 (3 points) is the statement “ Suppose that ? § ¡  ¥ Question 3 (3 points) Show that and § ¥ ¢ £ £ ¤ ¡ are equivalent. ¡ and § ¢ £ ¡¢ Question 5 (2 points) Let following sets.  ¥ ¥ ¥£¡ 4#32¥#%¨©¨§¦¤1 0 ¨ Question 6 (3 points) Prove or disprove that if A, B, and C are sets then § 09 [email protected] 5  @ 9 § ¨ § 0 D5 C @ 9 § 0 B9 A @ 9 9  @ 08 78  6 08 76 05 75  6 5  6 )¨('&¥#%##\$©#"¤!  ¨©¨§¦¤¢ ¥ ¥ ¥ ¥ ¥ ¥£¡ ¥ ¥ ¥ ¥ ¥£¡ ¨ ¨ 1. 6. 5. 4. 3. 2. 4 , and . Find each of the Question 7 (5 points) Name and describe the two axioms below: (a) § ¥ ¤ ¥ ©¤ ¡ ¡ ¤  (b) § ¨ ¨ ¢ ¤ £  § ¢ ¨ ¤ § ¨¢ § ¢ ¥ ¦¤ ¡ ¤ ¢ £ ¡ ¢ ¢  5 Question 8 (5 points) (a) List 5 axioms for Ordered Field of Natural Numbers. (b) Describe the Completenes and the Soundness Theorem 6 ...
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