# A Beginner's Guide to Discrete Mathematics by W. D. Wallis

By W. D. Wallis

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Solution. The truth value of x ∈ A is opposite that of x ∈ A, so the table is as follows. A T T T T F F F F B T T F F T T F F C T F T F T F T F A F F F F T T T T A∩B F F F F T T F F A∩C T F T F F F F F (A ∩ B) ∪ C T T T T T T T F There is no line with T in the second-last column and F in the last, so inclusion is proved. Practice Exercise. Prove that A ∩ B ∩ C ⊆ B ∩ (A ∪ C). Venn Diagrams It is common, and useful, to illustrate sets and operations on sets by diagrams. 3 Proof Methods in Set Theory 47 Fig.

29. 1012 . 30. 213 . 31. 23 . 32. 0314 . 33. 316 . 34. 16 . 35. 15 . 36. 228 . 37. 24 . 38. 448 . 39. 419 . 19 In Exercises 40 to 54, express the number in base 2. 40. 253. 41. 43. 42. 2. 43. 75. 44. 8. 45. 83. 46. 228. 47. 126. 48. 125. 49. 111. 50. 25. 51. 25. 52. 45. 53. 1819. 54. 8. In Exercises 55 to 69, express the number in base 6. 55. 1. 56. 1011. 57. 735. 58. 2. 59. 3. 60. 8. 61. 119. 62. 4. 63. 1104. 64. 205. 65. 4. 66. 2. 67. 3. 68. 77. 69. 4. In Exercises 70 to 84, express the number in hexadecimal (base 16) using the symbols 0, 1, .

128. 128 × 10−2 is not normalized, divide by 10 (and add 1 to the exponent). 313 × 10−1 . Notice that, again, a place is lost by truncation, and rounding to the nearer four-digit mantissa occurs. Practice Exercise. 644 × 10−4 . Sometimes an adjustment of the exponent can have extreme results. 004 × 10−1 , the exponent required is 3. 000 × 103 . Multiplication is carried out by multiplying mantissas and adding exponents— normalization may then be necessary. 23. 123 × 103 ). Solution. 710535. 710535× 105 .