3.2 Truth Tables for Negation, Conjunction, and Disjunction 107 73. It is false that if you work out then you will not gain weight. a) w g ( ) ∼ →∼ b) Negation 74. If dinner is ready then we can eat, or we cannot go to the restaurant. a) d e r ( ) → ∨ ∼ b) Disjunction 75. If the food has fiber or the food has vitamins, then you will be healthy. a) ∨ → f v h ( ) b) Conditional 76. If Corliss is teaching then Faye is in the math lab, if and only if it is not a weekend. a) c f w ( ) → ↔∼ b) Biconditional 77. You may take this course, if and only if you did not fail the previous course or you passed the placement test. a) c f p ( ) ↔ ∼ ∨ b) Biconditional 78. If the car has gas and the battery is charged, then the car will start. a) g b s ( ) ∧ → b) Conditional 79. The classroom is empty if and only if it is the weekend, or it is 7 a.m. a) c w s ( ) ↔ ∨ b) Disjunction Challenge Problems/Group Activities 80. An Ancient Question If Zeus could do anything, could he build a wall that he could not jump over? Explain your answer. Answers will vary. 81. a) Make up three simple statements and label them p q , , and r. Then write compound statements to represent ∨ ∧ p q r ( ) and ∨ ∧ p q r ( ). Answers will vary. b) Do you think that the statements for ∨ ∧ p q r ( ) and ∨ ∧ p q r ( ) mean the same thing? Explain. Answers will vary. Recreational Mathematics 82. Sudoku Refer to the Recreational Math box on page 100. Complete the following Sudoku puzzle. * 8 6 3 9 5 1 5 4 3 5 2 5 1 7 8 1 9 2 4 5 1 6 2 6 4 8 9 8 6 3 1 4 Research Activities 83. Legal Documents Obtain a legal document such as a will or rental agreement and copy one page of the document. Circle every connective used. Then list the number of times each connective appeared. Be sure to include conditional statements from which the word then was omitted from the sentence. 84. George Boole Write a report on the life and accomplishments of George Boole, who was an important contributor to the development of logic. In your report, indicate how his work eventually led to the development of the computer. 85. Mind Your P’s and Q’s The study of logic often involves the use of the letters p and q to represent statements. Research the use of the letters p and q in the study of logic. Also include a brief description of the various possible sources of the phrase “mind your p’s and q’s.” *See Instructor Answer Appendix Consider the following statement: Yogurt contains probiotics and whole wheat bread contains antioxidants. Under what conditions can the statement be considered true? Under what conditions can the statement be considered false? In this section, we will introduce a tool used to help us analyze such statements. Truth Tables for Negation, Conjunction, and Disjunction Roman Tiraspolsky/ Alamy Stock Photo SECTION 3.2 LEARNING GOALS Upon completion of this section, you will be able to: 7 Construct truth tables for statements involving negations, conjunctions, and disjunctions. 7 Understand an alternate method for constructing truth tables. 7 Determine truth values of statements without constructing truth tables. Why This Is Important We often encounter statements that include the words not, and, and or. These statements are called negations, conjunctions, and disjunctions, respectively. Understanding when such statements are true and when they are false can affect our daily lives. Making informed decisions when encountering these statements can have long-term effects on many aspects of our future.
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