Problem 1TTO: Decide if each statement is a tautology, a self-contradiction, or neither. (a) (p q) (p q) (b) (p... Problem 2TTO: Decide which two statements are logically equivalent. Then write examples of simple statements p and... Problem 3TTO: Write the negations of the following statements, using De Morgans laws. (a) I will study for this... Problem 4TTO Problem 5TTO: Write the converse, the inverse, and the contrapositive for the statement If you do well in math... Problem 6TTO: Write each statement in symbols. Let p = A student comes to class every day and q = A student gets a... Problem 1E: Explain the difference between a tautology and a self-contradiction. Problem 2E: Is every statement either a tautology or a self-contradiction? Why or why not? Problem 3E: Describe how to find the converse, inverse, and contrapositive of a conditional statement. Problem 4E: How can you decide if two statements are logically equivalent? Problem 5E: How can you decide if one statement is the negation of another? Problem 6E: Is a statement always logically equivalent to its converse? Explain. Problem 7E: For Exercises 716, determine which statements are tautologies, self-contradictions, or neither. 7.... Problem 8E: For Exercises 716, determine which statements are tautologies, self-contradictions, or neither. 8.... Problem 9E: For Exercises 716, determine which statements are tautologies, self-contradictions, or neither. 9.... Problem 10E: For Exercises 716, determine which statements are tautologies, self-contradictions, or neither. 10.... Problem 11E: For Exercises 716, determine which statements are tautologies, self-contradictions, or neither. 11.... Problem 12E: For Exercises 716, determine which statements are tautologies, self-contradictions, or neither. 12.... Problem 13E: For Exercises 716, determine which statements are tautologies, self-contradictions, or neither. 13.... Problem 14E: For Exercises 716, determine which statements are tautologies, self-contradictions, or neither. 14.... Problem 15E: For Exercises 716, determine which statements are tautologies, self-contradictions, or neither. 15.... Problem 16E: For Exercises 716, determine which statements are tautologies, self-contradictions, or neither. 16.... Problem 17E: For Exercises 1726, determine if the two statements are logically equivalent statements, negations,... Problem 18E: For Exercises 1726, determine if the two statements are logically equivalent statements, negations,... Problem 19E: For Exercises 1726, determine if the two statements are logically equivalent statements, negations,... Problem 20E: For Exercises 1726, determine if the two statements are logically equivalent statements, negations,... Problem 21E: For Exercises 1726, determine if the two statements are logically equivalent statements, negations,... Problem 22E: For Exercises 1726, determine if the two statements are logically equivalent statements, negations,... Problem 23E: For Exercises 1726, determine if the two statements are logically equivalent statements, negations,... Problem 24E: For Exercises 1726, determine if the two statements are logically equivalent statements, negations,... Problem 25E: For Exercises 1726, determine if the two statements are logically equivalent statements, negations,... Problem 26E: For Exercises 1726, determine if the two statements are logically equivalent statements, negations,... Problem 27E: For Exercises 2732, write the converse, inverse, and contrapositive of each. 27. p q Problem 28E: For Exercises 2732, write the converse, inverse, and contrapositive of each. 28. p q Problem 29E Problem 30E: For Exercises 2732, write the converse, inverse, and contrapositive of each. 30. (q r) (p r) Problem 31E: For Exercises 2732, write the converse, inverse, and contrapositive of each. 31. p (q r) Problem 32E Problem 33E: In Exercises 3342, use De Morgans laws to write the negation of the statement. 33. The patient is... Problem 34E: In Exercises 3342, use De Morgans laws to write the negation of the statement. 34. The experimental... Problem 35E: In Exercises 3342, use De Morgans laws to write the negation of the statement. 35. It is not cold... Problem 36E: In Exercises 3342, use De Morgans laws to write the negation of the statement. 36. I will walk in... Problem 37E: In Exercises 3342, use De Morgans laws to write the negation of the statement. 37. I will go to the... Problem 38E: In Exercises 3342, use De Morgans laws to write the negation of the statement. 38. The coffee is a... Problem 39E Problem 40E: In Exercises 3342, use De Morgans laws to write the negation of the statement. 40. I will go to... Problem 41E Problem 42E Problem 43E: In Exercises 4348, use De Morgans laws to write an equivalent statement. 43. It is not the case that... Problem 44E: In Exercises 4348, use De Morgans laws to write an equivalent statement. 44. Its totally false to... Problem 45E Problem 46E: In Exercises 4348, use De Morgans laws to write an equivalent statement. 46. This firms managing... Problem 47E: In Exercises 4348, use De Morgans laws to write an equivalent statement. 47. Its not true that my... Problem 48E: In Exercises 4348, use De Morgans laws to write an equivalent statement. 48. No way is that patient... Problem 49E: For Exercises 4955, let p = I need to talk to my friend and q = I will send her a text message.... Problem 50E: For Exercises 4955, let p = I need to talk to my friend and q = I will send her a text message.... Problem 51E Problem 52E: For Exercises 4955, let p = I need to talk to my friend and q = I will send her a text message.... Problem 53E Problem 54E: For Exercises 4955, let p = I need to talk to my friend and q = I will send her a text message.... Problem 55E Problem 56E Problem 57E: For Exercises 5762, write the converse, inverse, and contrapositive of the conditional statement.... Problem 58E: For Exercises 5762, write the converse, inverse, and contrapositive of the conditional statement.... Problem 59E: For Exercises 5762, write the converse, inverse, and contrapositive of the conditional statement.... Problem 60E Problem 61E: For Exercises 5762, write the converse, inverse, and contrapositive of the conditional statement.... Problem 62E Problem 63E Problem 64E: For Exercises 6368, write the negation of each statement in Exercises 5762. 58. If she does not earn... Problem 65E: For Exercises 6368, write the negation of each statement in Exercises 5762. 59. If the American Idol... Problem 66E Problem 67E: For Exercises 6368, write the negation of each statement in Exercises 5762. 67. Negation of Exercise... Problem 68E: For Exercises 6368, write the negation of each statement in Exercises 5762. 62. The politician will... Problem 69E Problem 70E Problem 71E Problem 72E Problem 73E Problem 74E Problem 75E Problem 76E: Try to write the negation of the biconditional p q by using only conjunctions, disjunctions, and... Problem 77E: Can you think of a true conditional statement about someone you know so that the converse is true as... Problem 78E Problem 79E Problem 80E format_list_bulleted