please, i need help. everything included tin he screenshots.

numbers 2, 4, 6, 8, 12. number 4 is related to number 3

F, and logical connectives. (a) I am awake implies that I work hard. 3. State the converse of each of the following implications. (b) I dream of home only if I am awake. (a) If 2 + 2 = 4, then I am not the Queen of England. (b) If I am not President of the United Sates, then I will (c) Working hard is sufficient for me to be awake. walk to work (d) Being awake is necessary for me not to dream of (c) If I am late, then I did not take the train to work. home. (d) If I have time and I am not too tired, then I will go to 2. Write each of the following statements in terms of p, 9, the store. 7, and logical connectives. (e) If I have enough money, then I will buy a car and I (a) I am not awake if and only if I dream of home. will buy a house. (b) If I dream of home, then I am awake and I work hard. 4. State the contrapositive of each implication in Exercise 3. 2.2 Conditional Statements 61 5. Determine the truth value for each of the following state- 17. Fill the grid so that each row, column, and marked 2 x 2 ments. square contains the letters M. A. T. H, with no repeats. (a) If 2 is even, then New York has a large population. (a) (b) (b) If 2 is even, then New York has a small population. M (c) If 2 is odd, then New York has a large population. (d) If 2 is odd, then New York has a small population. M In Exercises 6 and 7, let p, q, and r be the following state- H ments. p: I will study discrete structure; q: I will go to a movie; F: I am in a good mood. 6. Write the following statements in terms of p, q, r, and 18. Fill the grid so that each row, column, and marked 2 x 3 logical connectives. block contains 1, 2, 3. 4, 5, 6, with no repeats. (a) If I am not in a good mood, then I will go to a movie. (a) (b) I will not go to a movie and I will study discrete structures. 2 3 (c) I will go to a movie only if I will not study discrete 5 structures. (d) If I will not study discrete structures, then I am not in a good mood. 6 5 7. Write English sentences corresponding to the following statements. (a) ((~p)Aq) =r (b) r = (pvq) (c) (~r) = ((-qvp) (d) (q A (-p)) er (b) I 6 2 In Exercises 8 and 9, let p. q, r, and s be the following state- ments. p: 4 > 1: q: 4 2 2 8. Write the following statements in terms of p, q, r, and 5 logical connectives. (a) Either 4 > 1 or 4 2. 5 (c) It is not the case that 2 > 2 or 4 > 1. 9. Write English sentences corresponding to the following statements. (a) (PAS) = 9 (b) ~(rAq) (c) (~r) =p 19. Fill the grid so that each row, column, and marked 3 x 3 In Exercises 10 through 12, construct truth tables to determine block contains 1, 2, 3. 4, 5, 6, 7, 8, 9, with no repeats. whether the given statement is a tautology, a contingency, or an absurdity. 10. (a) pAmp (b) qv (-qAP)2.2 Conditional Statements 61 5. Determine the truth value for each of the following state- 17. Fill the grid so that each row, column, and marked 2 xx 2 ments. square contains the letters M. A, T. H, with no repeats. (a) If 2 is even, then New York has a large population. (a) (b) (b) If 2 is even. then New York has a small population. (c) If 2 is odd, then New York has a large population. (d) If 2 is odd, then New York has a small population. T M M In Exercises 6 and 7, let p, q, and r be the following state- H H ments. p: I will study discrete structure; q: I will go to a movie; F: I am in a good mood. 6. Write the following statements in terms of p, q, r, and 18. Fill the grid so that each row, column, and marked 2 x 3 logical connectives. block contains 1, 2, 3, 4, 5, 6, with no repeats. (a) If I am not in a good mood, then I will go to a movie. (a) (b) I will not go to a movie and I will study discrete structures. 2 (c) I will go to a movie only if I will not study discrete structures. (d) If I will not study discrete structures, then I am not in 6 1 5 a good mood. 6 5 7. Write English sentences corresponding to the following statements. (a) ((~p)Aq) = r (b) r = (pvq) (c) (~r) = ((-qvp) (d) (q A (-p)) er (b) I 6 2 In Exercises & and 9, let p. q, r, and s be the following state- ments. p: 4 > 1: q:4 2 2 8. Write the following statements in terms of p, q, r, and 5 logical connectives. (a) Either 4 > 1 or 4 2. (c) It is not the case that 2 > 2 or 4 > 1. 9. Write English sentences corresponding to the following statements. (a) (PAS) = q (b) ~(raq) (c) (~r) = p 19. Fill the grid so that each row, column, and marked 3 x 3 In Exercises 10 through 12, construct truth tables to determine block contains 1. 2, 3, 4, 5, 6. 7, 8. 9, with no repeats. whether the given statement is a tautology, a contingency, or an absurdity. 10. (a) pAsp (b) qv (-qAP) 9 3 11. (a) p = (q = p) (b) q = (q = p) 2 12. (a) (q A p) V (q A -p) 3 4 6 5 (b) (PAq) = P (c) p = (gap) 2 8 13. If p = q is false, can you determine the truth value of (~(p Aq)) = q? Explain your answer. 7 14. If p = q is false, can you determine the truth value of 9 1 (~p) v (p # q)? Explain your answer. 15. If p => q is true, can you determine the truth value of 3 (p Aq) = -q? Explain your answer. S 16. If p = q is true, can you determine the truth value of "(p = 4) A -p? Explain your