3.3 Truth Tables for the Conditional and Biconditional 125 m Stanford University Solution a) Let p q : 15 is an even number. : 29 is an even number. Then the statement “If 15 is an even number, then 29 is an even number” can be written p q. → Since 15 is not an even number, p is a false statement. Also, since 29 is not an even number, q is a false statement. We substitute F for p and F for q and evaluate the statement: p q F F T → → Therefore, “If 15 is an even number, then 29 is an even number” is a true statement. b) Let p q r : Stanford University is in California. : Wake Forest University is in Alaska. : Syracuse University is in Alabama. The original compound statement can be written p q r ( ) . ∧ ↔ By checking the Internet we can determine that Stanford University is in California, Wake Forest University is in North Carolina, and Syracuse University is in New York. Therefore, p is a true statement, but q and r are false statements. We will substitute T for p, F for q, and F for r and evaluate the compound statement: p q r ( ) (T F) F F F T ∧ ↔ ∧ ↔ ↔ Therefore, the original compound statement is true. 7 Now try Exercise 55 Example 7 Using Real Data in Compound Statements The graph in Fig. 3.2 was created using StatCrunch with data obtained from the website Oberlo.com. The graph shows the United States market share for various brands of cell phones in 2022. Use the data presented in the graph to determine the truth value of the following compound statements. U.S. Cell Phone Market Share 2022 Apple 57% Samsung 29% LG 2.5% Motorola 5% Others 6.5% Source: www.Oberlo.com Figure 3.2 a) If Apple has 57% of the U.S. market share and Samsung has 36% of the U.S. market share, then LG has 2.5% of the U.S. market share. MShieldsPhotos/Alamy Stock Photo
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