Section 3.4-Supawan King https://xlitemprod.pearsoncmg.com/api/v1/print/math Student: _____________________ Date: _____________________ Instructor: Supawan King Course: Math 102 Spring 2018 Assignment: Section 3.4 1. If your million dollar prize entry number matches the winning preselected number and you return the number before the deadline, you will win $1,000,000.00. Let p be the statement "your million dollar prize entry number matches the winning preselected number," let q be "you return the number before the deadline," and let r be "you will win $1,000,000.00." What is the claim in symbolic form? Choose the correct answer below. A. (p∧q)→r B. r→(p∨q) C. r→(p∧q) D. (p∧q)↔r E. (p∨q)→r F. (p∨q)↔r 2. Construct a truth table for the given statement. p→~q Fill in the truth table. (1) p q T T T F F T F F F (2) T F ~q (1) p→~q (2) (3) (4) (5) (6) (7) (8) (3) T F (4) T T F (5) F T (6) F T (7) T F (8) F T 3. Construct a truth table for the given statement. (q∧p)→(q∨p) Fill in the truth table. 1 of 4 p q T T T F F T F F q∧p q∨p (q∧p)→(q∨p) 2/15/18, 3:31 PM Section 3.4-Supawan King https://xlitemprod.pearsoncmg.com/api/v1/print/math 4. Construct a truth table for the given statement. (p→q)∧~q Fill in the truth table. p q T T T F F T F F p→q ~q (p→q)∧~q 5. Construct a truth table for the given statement. (p↔q)→p Fill in the truth table. p q T T T F F T F F p↔q (p↔q)→p 6. Determine the truth value for the given statement when p is false and q is true. ~p ↔ q True False 7. Determine the truth value for the statement when p is false, q is true, and r is true. q → (p ∧ r) True False 8. Determine the truth value for the given statement when p is true, q is true, and r is true. (~p ∧ q) ↔ ~r True False 9. Determine the truth value for the statement when p is false, q is false, and r is true. ~[(p → ~q) → (q ∨ ~p)] The statement is (1) (1) . true false 2 of 4 2/15/18, 3:31 PM Section 3.3-Supawan King Student: _____________________ Date: _____________________ https://xlitemprod.pearsoncmg.com/api/v1/print/math Instructor: Supawan King Course: Math 102 Spring 2018 Assignment: Section 3.3 1. Let p and q represent the following statements. p: 10 + 7 = 16 q: 5 × 6 = 30 Determine the truth value for the statement p∧q. Choose the correct truth value below. p∧q is false. p∧q is true. 2. Let p and q represent the following statements. p: 10 + 10 = 19 q: 3 × 10 = 30 Determine the truth value for the statement ~p∧q. Choose the correct truth value below. ~p∧q is false. ~p∧q is true. 3. Let p and q represent the following statements. p: 2 + 7 = 8 q: 10 × 5 = 100 Determine the truth value for the statement ~p∧~q. Choose the correct truth value below. ~p∧~q is false. ~p∧~q is true. 4. Let p and q represent the following statements. p: 9 + 6 = 15 q: 5 × 10 = 100 Determine the truth value for the statement p∨~q. Choose the correct truth value below. p∨~q is true. p∨~q is false. 1 of 10 2/15/18, 3:30 PM Section 3.3-Supawan King https://xlitemprod.pearsoncmg.com/api/v1/print/math 5. Complete the truth table for the given statement by filling in the required columns. s ∧ ~r r s T T T F F T F F ~r s ∧ ~r Complete the truth table. (1) r s T T T F F T F F ~r (2) T (1) (2) (3) (4) (5) (6) (7) (8) (3) T F s ∧ ~r F F (4) T T (5) F F (6) T T (7) F F (8) T T F 6. Complete the truth table for the given statement by filling in the required columns. q ∨ ~p p q T T T F F T F F ~p q ∨ ~p Complete the truth table. (1) p q T T T F F T F F F T 2 of 10 (2) T F ~p q ∨ ~p (1) (2) (3) (4) (5) (6) (7) (8) (3) F T (4) T F (5) F T (6) F T (7) F T (8) T F 2/15/18, 3:30 PM Section 3.3-Supawan King https://xlitemprod.pearsoncmg.com/api/v1/print/math 7. Complete the truth table for the given statement by filling in the required columns. ~(~q ∨ p) p T T F F ~q q T F T F ~q ∨ p ~(~q ∨ p) Complete the truth table. p q T T T F F T F F (1) (2) T F (9) ~q ~q ∨ p ~(~q ∨ p) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (3) F T (10) F (11) T (12) T F (5) F T T T (4) F T (6) F T (7) F T (8) F F T T F F 8. Construct a truth table for the given statement. (q ∨ p) ∧ ~q Complete the truth table. p (1) T T T F F T F F F (2) T (9) F T 3 of 10 ~q q∨p (q ∨ p) ∧ ~q (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) q F (3) T (10) T F (4) T F (11) (5) F T F T (12) F T (6) T F (7) F T (8) F T T F 2/15/18, 3:30 PM Section 3.3-Supawan King https://xlitemprod.pearsoncmg.com/api/v1/print/math 9. Construct a truth table for the given statement. ~q ∨ (p ∧ ~q) Complete the truth table. p q T T T F F T F F (1) (2) F T (9) ~q p ∧ ~q ~q ∨ (p ∧ ~q) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (3) F T (10) T F (4) T F (11) T T T (12) T F (5) F (6) F F (7) T F (8) F T T T F F 10. Construct a truth table for the given statement. (~q ∧ p) ∨ (p ∧ q) Complete the truth table. p q T T T F F T F F ~q ~q ∧ p p∧q (1) (2) (3) (4) (5) (6) (10) F T (16) (14) (15) (16) (2) T (9) (11) (12) (13) F (7) (8) (9) (1) (~q ∧ p) ∨ (p ∧ q) F (3) T (10) F T (4) T F (11) (5) T T F T F (12) (6) F T F (13) T (7) F F T (14) T (8) F F T (15) F T T F T F 4 of 10 2/15/18, 3:30 PM Section 3.3-Supawan King https://xlitemprod.pearsoncmg.com/api/v1/print/math 11. Refer to the following statement to answer parts (a) through (c) below. You did not do the laundry or you left the garage a mess. a. Write the statement in symbolic form. Assign letters to simple statements that are not negated. Choose the correct answer below. A. let p = you did not do the laundry and let q = you left the garage a mess; ~p ∨ q B. let p = you did not do the laundry and let q = you left the garage a mess; ~p ∧ q C. let p = you did the laundry and let q = you left the garage a mess; ~p ∧ q D. let p = you did the laundry and let q = you left the garage a mess; ~p ∨ q b. Construct a truth table for the symbolic statement in part (a). p q T T T F F T F F ~p ∨ q ~p (1) (2) (3) (4) (5) (6) (7) (8) c. Use the truth table to indicate one set of conditions that make the compound statement true, or state that no such conditions exist. Choose the correct answer below. A. The statement is true when p is false and q is true. B. The statement is true for all conditions. C. There are no conditions for which the statement is true. D. The statement is true when p is true and q is false. (1) F T 5 of 10 (2) F T (3) T F (4) T F (5) F T (6) T F (7) T F (8) T F 2/15/18, 3:30 PM Section 3.3-Supawan King https://xlitemprod.pearsoncmg.com/api/v1/print/math 12. Refer to the following statement to answer parts (a) through (c) below. The student is intelligent and an overachiever, and not an overachiever. a. Write the statement in symbolic form. Assign letters to simple statements that are not negated. Choose the correct answer below. A. let p = The student is intelligent and let q = The student is not an overachiever; (p ∨ q) ∨ ~q B. let p = The student is intelligent and let q = The student is an overachiever; (p ∧ q) ∧ ~q C. let p = The student is intelligent and let q = The student is an overachiever; (p ∨ q) ∨ ~q D. let p = The student is intelligent and let q = The student is not an overachiever; (p ∧ q) ∧ ~q b. Construct a truth table for the symbolic statement in part (a). p q T T T F F T F F p∧q ~q (p ∧ q) ∧ ~q (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) c. Use the truth table to indicate one set of conditions that make the compound statement true, or state that no such conditions exist. Choose the correct answer below. A. The statement is true when p is true and q is false. B. There are no conditions for which the statement is true. C. The statement is true when p is true or q is false. D. The statement is true for all conditions. (1) F (2) T (9) F T 6 of 10 T (3) F (10) F T (4) F T (11) (5) T F T F (12) F T (6) F T (7) F T (8) F T F T 2/15/18, 3:30 PM Section 3.2-Supawan King https://xlitemprod.pearsoncmg.com/api/v1/print/math Student: _____________________ Date: _____________________ Instructor: Supawan King Course: Math 102 Spring 2018 Assignment: Section 3.2 1. Let p and q represent the following statements. p: You are happy. q: You have a lot of money. Translate the following statement into symbols. You are not happy and you are wealthy. The statement in symbolic form is . 2. Let p and q represent the following simple statements: p: I work hard. q: It is time to sleep. Write the following compound statement in its symbolic form. I work hard and it is not time to sleep. The symbolic form is . 3. Let p and q represent the following simple statements: p: I study. q: The chair is broken. Write the following compound statement in its symbolic form. If I do not study, then the chair is not broken. Choose the correct symbolic form below. A. p → q B. p → ~q C. ~p → q D. ~p → ~q 4. Let p and q represent the following simple statements. p: You are human. q: You have horns. Write the following compound statement in symbolic form. You have horns if you are not human. Choose the correct symbolic form below. A. q∧~p B. ~p→q C. ~p↔q D. q→~p 1 of 5 2/15/18, 3:30 PM Section 3.2-Supawan King https://xlitemprod.pearsoncmg.com/api/v1/print/math 5. Let p and q represent the following simple statements. p: I pass the course. q: I do my homework. Write the following compound statement in symbolic form. I pass the course if and only if I do my homework. Choose the correct symbolic form below. A. p↔q B. p∧q C. p↔~q D. p→q 6. Use letters to represent each non-negated simple statement and rewrite the given compound statement in symbolic form. If my car is in working order then I can go to the store, and I cannot go to the store. Choose the correct symbolic form below. Let p represent the simple sentence "My car is in working order" and q represent "I c A. (p→q)∧~q B. p→(q∧~q) C. (p∧q)→~q D. (p↔q)∨~q 7. Consider the statements. p: The belt is red. q: The vest is black. Rewrite the statement ~p∧~q in English. What is the English version of the statement ~p∧~q? A. The belt is not red or the vest is not black. B. If the belt is not red, then the vest is not black. C. The belt is red and the vest is not black. D. The belt is not red and the vest is not black. 8. Let p and q represent the following simple statements: p: The play is boring. q: It is time to sleep. Write the symbolic statement p ↔ ~q in words. Choose the correct sentence below. A. If the play is boring, then it is not time to sleep. B. The play is boring if and only if it is not time to sleep. C. If the play is boring, then it is time to sleep. D. It is time to sleep if and only if the play is not boring. 2 of 5 2/15/18, 3:30 PM Section 3.2-Supawan King https://xlitemprod.pearsoncmg.com/api/v1/print/math 9. Let q and r represent the following simple statements. q: It is Saturday. r: We are watching cartoons. Write the symbolic statement q∧~r in words. Choose the correct sentence below. A. If it is not Saturday, then we are watching cartoons. B. It is not Saturday and we are watching cartoons. C. It is Saturday or we are not watching cartoons. D. It is Saturday and we are not watching cartoons. 10. Let p, q, and r represent the following simple statements: p: The taxes are high. q: The chair is broken. r: It is time to sleep. Write the following compound statement in its symbolic form. The taxes are high and the chair is broken, or it is time to sleep. The symbolic form is . 11. Let p, q, and r represent the following simple statements. p: The temperature is below 45°. q: We finished eating. r: We go to the slope. Write the symbolic statement (r∧p)→q in words. Choose the correct sentence below. A. If we go to the slope or the temperature is below 45°, then we have finished eating. B. If we go to the slope, then the temperature is below 45° and we have finished eating. C. If we go to the slope and the temperature is below 45°, then we have finished eating. 12. Let p, q, and r represent the following simple statements. p: The temperature is below 40°. q: We finished writing. r: We go to the slope. Write the symbolic statement r∧(p→q) in words. Choose the correct sentence below. A. If we go to the slope, then the temperature is below 40° and we have finished writing. B. We go to the slope, and if the temperature is below 40° then we have finished writing. C. If we go to the slope and the temperature is below 40°, then we have finished writing. 3 of 5 2/15/18, 3:30 PM Section 3.2-Supawan King https://xlitemprod.pearsoncmg.com/api/v1/print/math 13. Write the compound statement in symbolic form. Let letters assigned to the simple statements represent English sentences that are not negated. If commas do not appear in compound English statements, use the dominance of connectives to show grouping symbols (parentheses) in symbolic statements. If the lines go down or the transformer blows then we do not have power. Choose the correct symbolic form below. Let p represent the simple sentence "The lines go down," q represent the simple sentence "The transformer blows," and r represent the simple sentence "We have power." A. (p∨q)→ ~r B. (p∧q)→ ~r C. p∨(q↔ ~r) D. p∨(q→r) 14. Let p, q, and r represent the following simple statements. p: The temperature is below 35°. q: We finished working. r: We go to the ice rink. Write the symbolic statement ~p→ ~q∨~r in words. Choose the correct sentence below. A. If the temperature is not below 35° or we have not finished working, then we do not go to the ice rink. B. If the temperature is not below 35°, then we have not finished working and we do not go to the ice rink. C. If the temperature is not below 35°, then we have not finished working or we do not go to the ice rink. 15. Write the compound statement in symbolic form. Let letters assigned to the simple statements represent English sentences that are not negated. If commas do not appear in compound English statements, use the dominance of connectives to show grouping symbols (parentheses) in symbolic statements. I get sick if and only if it's not true that both I eat my fruit and I eat red meat. Choose the correct symbolic form below. Let p represent the simple sentence "I eat my fruit," q represent the simple sentence "I eat red meat," and r represent the simple sentence "I get sick." A. ~p→(r∨q) B. r↔~(p∧q) C. r↔~(p∨q) D. ~r→(p∧q) 4 of 5 2/15/18, 3:30 PM
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