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Siegel's modular forms and dirichlet series. Course given at by Hans Maass

By Hans Maass

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Sample text

The sentence is either true or it is false, and it is not both true and false, so it is a statement. 3. We do not know whether the given sentence is true or false, but we know that the sentence is either true or false and that it is not both true and false. Thus the sentence is a statement. 4. Since the square of any real number is either positive or zero, this is a true sentence. Thus the sentence is a statement. 5. The sentence “Lock the car” is a command. It is not a statement. 6. The sentence “Clark Kent is Superman” is either true or false, so it is a statement.

Because both spout openings are at the same height, the maximum number of cups that can hold is the same. 39. (q ∧ r) → ~p 41. s → (q ∧ ∼ p) 43. 3 > 1 is true, so the statement is true. 45. (−1)50 = 1 is true and (−1)99 = −1 is true, so the statement is true. 47. –5 > –11, so the statement is true. 49. “2 is an even number” is a true statement, so the statement is true. 51. All cats have claws. 53. Some classic movies were not first produced in black and white. 55. Some of the numbers were even numbers.

71. a. 61. When x = –1, the antecedent is true and the consequent is false. So this is a false statement. 62. When x = 2 and y = –2, the antecedent is true and the consequent is false. So this is a false statement. 63. If a real number has a nonrepeating, nonterminating decimal form, then the real number is irrational. 64. If you are a politician, then you are well known. 65. If I can sell my condominium, then I can buy the house. 66. If a number is divisible by 9, then the number is divisible by 3.

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