6-Sets & Set Operations (2.1-2.2) - EECS 210 Discrete...

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Sets & Set Operations David O. Johnson EECS 210 (Fall 2016) 1 EECS 210 Discrete Structures David O. Johnson Fall 2016
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Reminders Exam 1: Thursday, September 15 More later Homework 2: Thursday, September 22 (Located in Course Documents on BlackBoard) Note: New procedure for submitting homework! Paper instead of electronic Include your name and KU ID on the first page Homework is due at the beginning of your Thursday lecture in the classroom. I will give them back to you during the following Thursday lecture. Late Homework assignments must be turned in electronically by emailing to Cheng Gao (c[email protected]) 10% off if turned in after your Thursday lecture 50% off if turned in after Friday, 11:59 PM 0%, if turned in after the solutions are posted Late homework will be graded at the GTA’s convenience Sets & Set Operations David O. Johnson EECS 210 (Fall 2016) 2
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Any Questions? Sets & Set Operations 3 David O. Johnson EECS 210 (Fall 2016)
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Exam 1 Review Construct a truth table for a proposition (Section 1.1): 12 points Construct a combinatorial circuit using inverters, OR gates, and AND gates( Section 1.2): 12 points Use a truth table to prove two propositions are equivalent (Section 1.3): 12 points Given the definition and domain of a predicate, P ( x ), evaluate it for specific members of the domain, e.g., P (-1) and for the universal and existential quantifiers, e.g., x ¬ P ( x ) (Section 1.4): 12 points Given the definition and domain of a predicate, P ( x,y ), evaluate it for specific members of the domain, e.g., P (-1,y) and for nested universal and existential quantifiers, e.g., y xP ( x , y ) (Section 1.5): 12 points Sets & Set Operations David O. Johnson EECS 210 (Fall 2016) 4
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Exam 1 Review 2 questions on Proof Reasons (Sections 1.6 and 1.7): 10 points each Example: Fill-in the blanks with the following letters to indicate which Reasons were used in the proofs. Except for Premises, the numbers in parentheses are the steps which the Reasons were applied to (Hint: The Reason for the ones without numbers is “Premise”): Sets & Set Operations David O. Johnson EECS 210 (Fall 2016) 5 A. Premise B. Modus ponens C. Modus tollens D. Hypothetical syllogism E. Disjunctive syllogism F. Addition G. Simplification H. Conjunction I. Resolution J. Contrapositive K. De Morgan’s law L. Double negative M. Universal instantiation N. Universal generalization O. Existential instantiation P. Existential generalization A O G A M B G H P
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Exam 1 Review 2 questions on Proof Methods (Section 1.8): 10 points each Example: For the two previous proofs, which of the following proof methods were used? Circle the proof methods used. There may be one or more proof methods. (2 points for each correct answer) Correct = It is circled and it is supposed to be circled; or it is NOT circled and it is NOT supposed to be circled.
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  • Fall '12
  • kato
  • Set Theory, Natural number, David O. Johnson EECS, O. Johnson EECS

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