SG4eCh2 - Chapter 2: The Logic of Compound Statements...

Info iconThis preview shows pages 1–3. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 2: The Logic of Compound Statements Section 2.1 9. ( n k ) ( n k ) 15. p q r q q r p ( q r ) T T T F T T T T F F F F T F T T T T T F F T T T F T T F T F F T F F F F F F T T T F F F F T T F The truth table shows that p ( q r ) and ( p q ) ( p r ) always have the same truth values. Therefore they are logically equivalent. This proves the distributive law for over . 24. p q r p q p r ( p q ) ( p r ) ( p q ) r T T T T T T T T T F T F T F T F T T T T T T F F T F T F F T T T F T T F T F T F T F F F T F F F F F F F F F F F | {z } different truth values The truth table shows that ( p q ) ( p r ) and ( p q ) r have different truth values in rows 2, 3, and 6. Hence they are not logically equivalent. 30. The dollar is not at an all-time high or the stock market is not at a record low. 33.- 10 x or x 2 39. The statements logical form is ( p q ) (( r s ) t ) , so its negation has the form (( p q ) (( r s ) t )) ( p q ) (( r s ) t )) ( p q ) ( ( r s ) t )) ( p q ) (( r s ) t )) . Thus a negation is ( num orders 50 or num instock 300) and ((50 > num orders or num orders 75) or num instock 500). 4 Solutions for Exercises: The Logic of Compound Statements 42. p q r p q p q q r (( p q ) ( q r )) (( p q ) ( q r )) q T T T F F F T F F T T F F F F F F F T F T F T F F F F T F F F T F F F F F T T T F T T T F F T F T F T F F F F F T T T F F F F F F F T T F F F F | {z } all F s Since all the truth values of (( p q ) ( q r )) q are F , (( p q ) ( q r )) q is a contradiction. 45. Let b be Bob is a double math and computer science major, m be Ann is a math major, and a be Ann is a double math and computer science major. Then the two statements can be symbolized as follows: a . ( b m ) a and b . ( b a ) ( m b ) . Note : The entries in the truth table assume that a person who is a double math and computer science major is also a math major and a computer science major. b m a a b m m b b a ( b a ) ( b m ) a ( b a ) ( m b ) T T T F T T T F F F T T F T F T F T T T T F T F T F T F F F T F F T F F F T F F F T T F F F F T F F F T F T F F F T F F F F T F F F F T F F F F F T F F F T F F | {z } same truth values The truth table shows that ( b m ) a and ( b a ) ( m b ) always have the same truth values. Hence they are logically equivalent....
View Full Document

Page1 / 8

SG4eCh2 - Chapter 2: The Logic of Compound Statements...

This preview shows document pages 1 - 3. Sign up to view the full document.

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