solutions2problems

solutions2problems - 1 Solutions Problem 1.1 Indicate which...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Solutions Problem 1.1 Indicate which of the following sentences are propositions. a. 1,024 is the smallest four-digit number that is perfect square. b. She is a mathematics major. c. 128 = 2 6 d. x = 2 6 . Solution. a. Proposition with truth value (T). Note that 32 2 = 1024 and 31 2 = 961 . b. Not a proposition since the truth or falsity of the sentence depends on the reference for the pronoun she. For some values of she the statement is true; for others it is false. c. A proposition with truth value (F). d. Not a proposition Problem 1.2 Consider the propositions: p: Juan is a math major. q: Juan is a computer science major. Use symbolic connectives to represent the proposition Juan is a math major but not a computer science major. Solution. p q Problem 1.3 In the following sentence is the word or used in its inclusive or exclusive sense? A team wins the playoffs if it wins two games in a row or a total of three games. Solution. Exclusive 2 Problem 1.4 Write the truth table for the proposition: ( p ( p q )) ( q r ) . Solution. Let s = ( p ( p q )) ( q r ) . p q r p r p q q r ( q r ) p ( p q ) s T T T F F T F T T T T T F F T T T F T F T F T F F F F T T T T F F F T F F T T T F T T T F T F T T T F T F T T T T F T F F F T T F T F T T T F F F T T T F T T T Problem 1.5 Let t be a tautology. Show that p t t. Solution. p t p t T T T F T T Problem 1.6 Let c be a contradiction. Show that p c p. Solution. p c p c T F T F F F Problem 1.7 Show that ( r p ) (( r ( p q )) ( r q )) p q. 3 Solution. Let s = ( r ( p q )) ( r q ) . p q r r p r q r ( p q ) s ( r p ) s p q T T T T T T T T T T T F T T T T T T T F T T T F F F F T F F T F T F F F F T T T T F F F F F T F F T T F F F F F T T T F F F F F F F F F T F F F Problem 1.8 Use De Morgans laws to write the negation for the proposition:This com- puter program has a logical error in the first ten lines or it is being run with an incomplete data set. Solution. This computer program is error free in the first ten lines and it is being run with complete data. Problem 1.9 Use De Morgans laws to write the negation for the proposition:The dollar is at an all-time high and the stock market is at a record low. Solution. The dollar is not at an all-time high or the stock market is not at a record low. Problem 1.10 Assume x R . Use De Morgans laws to write the negation for the proposition:0 x >- 5 . Solution. x - 5 or x > . 4 Problem 1.11 Show that the proposition s = ( p q ) ( p ( p q )) is a tautology....
View Full Document

Page1 / 127

solutions2problems - 1 Solutions Problem 1.1 Indicate which...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online