# Difference: EDMExamISampleTest (5 vs. 6)

#### Revision 62011-03-15 - JimSkon

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 META TOPICPARENT name="ElementaryDiscreteMath2011"

# Elementary Discrete Math

###### Sample Exam I
Line: 39 to 39

 (h) Double complement law ¬( ¬x) = x (i) DeMorgan's laws ¬(x ∧ y) = ¬x ∨ ¬y ¬(x ∨ y) = ¬x ∧ ¬y
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 (j) Absorbtion (x ∨ y) ∧ x = x (x ∧ y) ∨ x = x

Line: 185 to 187
(b) P({a,b,c,d}), where P denotes the power set.
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(c) {1,3,5,7...}.
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Infinity
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(c) {1,3,5,7...}.
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(d) A x B where A = {1,2,3,4,5} and B = {1,2,3}.
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Line: 276 to 278
18. Simplify the following using the properties of set operation:
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1. (A ∪ B)c ∩. (A c ∩ B c)
2. (A ∪ (B ∩ A))
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1. (A ∪ B)c ∩ (A c ∩ B c) =
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(A ∪ B)c ∩ (A ∪ B )c = (A ∪ B)c = Ac ∪ Bc
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2. (A ∪ (B ∩ A)) =
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(A ∪ B) ∩ (A ∪ A ) = (A ∪ B) ∩ (A ) = A
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1. (A ∪ (B ∩ A)) c ∩ ((C c ∪ B c) ∩ A c) c

Line: 293 to 295
a. A = {x |x N ∧ (∀y,w : y,w N ∧y ≠ 1 ∧ w ≠ 1 ∧ xyw ) } ( N is the set of natural numbers)
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Prime numbers, infinite
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b. A = {x |x N ∧ x < 100 ∧ (∃y: y N ∧ x = 3y) } ( N is the set of natural numbers)
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multiples of 3 {3, 6, 9, ... 99}, 33
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b. A = {x |x N ∧ x < 100 ∧ (∃y: y Nx = 3y) } ( N is the set of natural numbers)
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multiples of 3 {3, 6, 9, ... 99}, 33
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c. A = {x |x Z ∧ (∃y: y Zx = y2) } ( Z is the set of Integers)

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Squares {0, 1, 2, 4, 9, 16, ...}, ∞
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-- JimSkon - 2011-03-14

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