1301 3.2_3.3 Truth Tables UTA
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Instructor: Florencio Ricohermoso, Elizabeth Student: iR Legault, Juan Silva, Math Dept . . Date: 03/25/24 Course: 2242-MATH-1301-502- Assignment: 3.2/3.3 Truth Tables CONTEMPORARY MATH Fill in the blank. The negation of p, ~p, will always have the truth value of p. The negation of p, ~p, will always have the opposite truth value of p. 2. Fillin the blank. The conjunction p A qis true only when both p and q are The conjunction p A q is true only when both p and g are true. 3. Fillin the blank with an appropriate word, phrase, or symbol. The conditional statement p — q is only when p is true and q is false. The conditional statement p — q is only false when p is true and q is false. 4. Fill in the blank with an appropriate word, phrase, or symbol. The biconditional statement p < q is only when p and g have the same truth value. The biconditional statement p <> q is true only when p and q have the same truth value. 5. Select the correct choice that completes the sentence below. A compound statement that is always true is known as a tautology. 6. Fill in the blank with an appropriate wor_d, phrase, or symbol. A compound statement that is always false is known as a A compound statement that is always false is known as a self-contradiction. 7. Construct a truth table for the following statement. ~qv~p Complete the truth table. q P ~q ~p ~qv~p T T F F F T F F T T F 0 T F T F F T T T
8. Construct a truth table for the statement. ~(av~p) Complete the truth table. p | a| ~(v~p) T| T F T|F T FIT F F|F F 9. Construct a truth table for the given statement. -~ x_)y Fill in the truth table. X y ~X y ~X—=y T T F I T T F F F T F T T T T F F i F F 10. Construct a truth table for the statement (b—a)« a. Complete the truth table. a|b| b—a| (b—a)—a T| T T T T|F T T FI|T F T F|F T F 11. Write the following compound statement in symbolic form and construct a truth table. "The tea is hot or the napkins have not been put out." p: The tea is hot. q: The napkins have been put out. Determine the symbolic form of the compound statement and construct a truth table for the symbolic expression. PV ~q N4+ nm|4|m|4|a || |4
12. Write the statement in symbolic form and construct a truth table. It is false that the vehicle is white, but the vehicle is not a car. Let statement p be "The vehicle is white." Let statement q be "The vehicle is a car.” Identify the symbolic form of the given statement, and then complete the truth table. P | q ~(pA~q) TI| T T T | F F F T T F|F T 13. Use the graph, which shows the number of hours Americans sleep, to determine the Hours of Sleep truth value of each simple statement. Then determine the truth value of the compound B 4 or fewer, 4% statement. B 5 hours, 9% Wl 6 hours, 25% 7 hours, 30% [ 8 hours or more, 32% It is false that 9% of Americans get 7 hours of sleep each night and 30% get 5 hours of sleep each night. What is the truth value of the simple statement "9% of Americans get 7 hours of sleep each night"? * False X True What is the truth value of the simple statement "30% get 5 hours of sleep each night"? * False X True What is the truth value of the compound statement "It is false that 9% of Americans get 7 hours of sleep each night and 30% get 5 hours of sleep each night"? X False * True YOU ANSWERED: True True False
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12. Write the statement in symbolic form and construct a truth table. It is false that the vehicle is white, but the vehicle is not a car. Let statement p be "The vehicle is white." Let statement q be "The vehicle is a car." Identify the symbolic form of the given statement, and then complete the truth table. P | a ~(pA~q) T T T T|F F F T T F|F T 13. Use the graph, which shows the number of hours Americans sleep, to determine the Hours of Sleep truth value of each simple statement. Then determine the truth value of the compound M 4 or fewer, 4% statement. M 5 hours, 9% Il 6 hours, 25% [ 7 hours, 30% [ 8 hours or more, 32% It is false that 25% of Americans get 6 hours of sleep each night and 4% get 4 or fewer hours of sleep each night. What is the truth value of the simple statement "25% of Americans get 6 hours of sleep each night"? M True False What is the truth value of the simple statement "4% get 4 or fewer hours of sleep each night"? ¥ True False What is the truth value of the compound statement "It is false that 25% of Americans get 6 hours of sleep each night and 4% get 4 or fewer hours of sleep each night"? v False True b
14. Use the graph, showing the results of a survey of the hours of sleep a group of people gets each night, to determine the truth value of each simple statement in the given compound statement. Then determine the truth value of the compound statement. Over one-quarter of people in the group get 6 or fewer hours of sleep each night and over one-half get 6 hours of sleep each night. What is the truth value of the first simple statement? False ¥ True What is the truth value of the second simple statement? X True * False What is the truth value of the compound statement? ¥ False True YOU ANSWERED: True Hours of Sleep B 4 or fewer, 4% Wl 5 hours, 9% M 6 hours, 25% [ 7 hours, 30% [ 8 hours or more, 32% 15. Translate the following statement into symbols. Then construct a truth table for the compound statement and indicate under what conditions the compound statement is true. You mowed the lawn or you did not leave the garage a mess. p: You mowed the lawn. q: You left the garage a mess. Write the compound statement in symbolic form and complete the truth table below. PV ~q n|m| 4| 4| m| 4| | H|a A 4|4 Use the truth table to determine the set of conditions that make the compound statement true. Choose the correct answer below. *A. The statement is true whenever p is true or q is false, and is false otherwise. XB. The statement is true whenever p and q are both true, and is false otherwise. C. The statement is true whenever p and q are both false, and is false otherwise. D. The statement is true whenever p is false and q is true, and is false otherwise. E. The statement is true whenever p is true or q is true, and is false otherwise. YOU ANSWERED: B.
14. Use the graph, showing the results of a survey of the hours of sleep a group of people Hours of Sleep gets each night, to determine the truth value of each simple statement in the given W 4 or fewer, 4% compound statement. Then determine the truth value of the compound statement. W 5 hours, 9% B 6 hours, 25% B 7 hours, 30% [ 8 hours or more, 32% Over one-quarter of people in the group get 6 or fewer hours of sleep each night and over one-half get 6 hours of sleep each night. What is the truth value of the first simple statement? False ¥ True What is the truth value of the second simple statement? X True * False What is the truth value of the compound statement? ¥ False True YOU ANSWERED: True 15. Translate the following statement into symbols. Then construct a truth table for the compound statement and indicate under what conditions the compound statement is true. You mowed the lawn or you did not leave the car a mess. p: You mowed the lawn. Q: You left the car a mess. Write the compound statement in symbolic form and complete the truth table below. p q PV ~q T o T T F T F T F F F T Use the truth table to determine the set of conditions that make the compound statement true. Choose the correct answer below. A. The statement is true whenever p and g are both true, and is false otherwise. ¥ B. The statement is true whenever p is true or q is false, and is false otherwise. C. The statement is true whenever p and g are both false, and is false otherwise. D. The statement is true whenever p is false and q is true, and is false otherwise. E. The statement is true whenever p is true or g is true, and is false otherwise. Hh
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16. Determine whether the statement is an implication. ~r—r Determine whether the statement ~r — ris an implication. A. The statement is an implication. V B. The statement is not an implication. * + C. ltis impossible to tell. 17. Determine the truth value of the statement (p A ~q) V r using the following conditions. a) p is false, q is false, and r is false. b) p is true, q is false, and r is false. a) If p is false, q is false, and r is false, what is the truth value of (p A ~q) v r? ¥ False True b) If p is true, q is false, and r is false, what is the truth value of (p A ~q) vV ? False ¥ True 18. Determine the truth value of the statement (p A q) A ~r using the following conditions. a) p is false, q is true, and r is true. b) p is true, q is false, and r is false. a) If pis false, q is true, and r is true, what is the value of (p A Q) A ~1? f" False True b) If p is true, q is false, and r is false, what is the value of (p A Q) A ~1? ¥ False True 19. If ais false, b is true, and ¢ is true, find the truth value of the statement. a—>(b—c) Select the truth value of a — (b — c) when a is false, b is true, and ¢ is true. Choose the correct answer below.
20. If pistrue, qis true, and ris true, find the truth value of the statement. (PAd)eo(QV ~r) Choose the correct answer below. A. False because (p A q) is false and (q v ~r) is false. B. True because (p A q) is false and (g v ~r)is false. ¥ C. True because (pAQ)istrue and (q v ~r) is true. D. False because (p A q) is true and (q v ~r) is true.