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# Math and Humanity MATH 116

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This 4 page Class Notes was uploaded by Angelina Steuber on Monday October 19, 2015. The Class Notes belongs to MATH 116 at Radford University taught by Stephen Corwin in Fall. Since its upload, it has received 11 views. For similar materials see /class/224678/math-116-radford-university in Mathematics (M) at Radford University.

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Date Created: 10/19/15

Math 1 16 Test 3 Review Logic Negations of a statement 1 Negate the following statements a All dogs are friendly Negation Some dogs are not friendly b The book is blue Negation The book is not blue Types of statement Conditionals Conditional A gt B Converse B gt A Inverse N A gt B Contrapositive N B gt A 2 Given the statement If two lines cut by a transversal are parallel then the corresponding angles formed are congruent a State the converse If the corresponding angles formed are congruent then the two lines cut by a transversal are parallel b State the inverse If two lines are cut by a transversal are not parallel then the corresponding angles are not congruent c State the contrapositive If the corresponding angles formed are not congruent then the two lines cut by a transversal are not parallel Truth Tables 3 Complete each truth table a Av N B gt A B F bB gtAB B F 4 Show that A gt B and N A v B are equivalent statements AaB NAVB Since the two statements get the same result in their truth tables the arguments are equivalent 5 Write the argument in symbolic form then determine if the following argument is valid or invalid If Jane does her Calculus homework every night then she will do well in her Calculus class A gt B Jane did not do well in her Calculus class N B Therefore Jane did not do her Calculus homework every night N A S olution If Jane does her Calculus homework every night then she will do well in her Calculus class A gt B Jane did not do well in her Calculus class N B Therefore Jane did not do her Calculus homework every night N A Argument in symbolic form A gt BA N B gtN A A B NA NB gtB gtB NB Since the argument is a tautology the argument is valid 6 Negate using De Morgan s Law a Av N B N Av N B Solution N AA N N B NAAB b N AA N B N N AA N B Solution N N Av N N B A v B 7 LL A abcdef B abcd C cdefgh D m U abcdefghijklm a Find AUB abcdef b Find AnC cdef c Is C CA No d Is B CA Yes e What is nA nA 6 f What is nA UB nA U B 6 g Find A39 A ghijklm 7 List all the subsets of the set 01 0101 8 How many subsets does a set with 13 elements have 2 213 8192

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