Difference: EDMExamISampleTest (4 vs. 5)

Revision 52011-03-15 - JimSkon

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META TOPICPARENT name="ElementaryDiscreteMath2011"

Elementary Discrete Math

Sample Exam I
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  (a) p → ( pq) ... Close
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neither
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Changed:
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(b) q ∧ ( pq) ... Close
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contradiction
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(b) q ∧ ( pq) ... Close
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contradiction
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  (c) (( pp) → q) ... Close
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neither
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Line: 193 to 193
  (f) P(A), where A is the power set of {a,b,c}. ... Close
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256
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Changed:
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(g) A x B, where A = {a,b,c} and B = . ... Close
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0
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(g) A x B, where A = {a,b,c} and B = ∅. ... Close
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0
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  (h) {x|x ∈ N and 4x2 - 1 = 0}. ... Close
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0
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  (b) {{a}} ⊆ P(A)
Changed:
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(c) ⊆ A
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(c) ∅ ⊆ A
 
Changed:
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(d) {} ⊆ P(A)
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(d) {∅} ⊆ P(A)
 
Changed:
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(e) ⊆ A x A
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(e) ∅ ⊆ A x A
  (f) {a,c} ∈ A
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  (e) {x | x ∈ Z and x2 < 80}.
Changed:
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(a) 1, (b) 2^(2^3)=256, (c) ,(d) 24, (e) 17

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(a) 1, (b) 2^(2^3)=256, (c) infinity ,(d) 24, (e) 17
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... Close
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(a) 1, (b) 2^(2^3)=256, (c) ∞ ,(d) 24, (e) 17
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Changed:
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16. Let A = { 2,4,6,8 } B = {4, 7} C = {, {4, 7}}
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16. Let A = { 2,4,6,8 } B = {4, 7} C = {∅, {4, 7}}
  Show the following:
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  b. A ∩ B = ... Close
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{ 4 }
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Changed:
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c. A ∪ C = ... Close
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{{ 2,4,6,8, , {4, 7}}
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>
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c. A ∪ C = ... Close
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{{ 2,4,6,8, ∅, {4, 7}}
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Changed:
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d. A ∩ C = ... Close
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d. A ∩ C = ... Close
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  e. A - B = ... Close
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{2, 6, 8}
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Changed:
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f. C - = ... Close
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{, {4, 7}}
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>
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f. C - ∅ = ... Close
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{∅, {4, 7}}
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g. ∅ - C = ... Close

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Changed:
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g. - C = ... Close
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h. C ∪ (A ∩ B) = ... Close
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{4, ∅, {4, 7}}
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Changed:
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h. C ∪ (A ∩ B) = ... Close
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{4, , {4, 7}}
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>
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i. P(A) = ... Close
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{{},{2},{2,4},{2,4,6},{2,4,6,8},{2,4,8},{2,6},{2,6,8},{2,8},{4},{4,6},{4,6,8},{4,8},{6},{6,8},{8}}
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Added:
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j. B x C = ... Close
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{(4, ∅), (4, {4, 7}), (7, ∅), (7, {4, 7}) }
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17. Show Venn Diagrams for each of the above.

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  1. (A ∪ (B ∩ A)) c ∩ ((C c ∪ B c) ∩ A c) c

Changed:
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19. Prove the following using a. set builder notation and b Membership tables
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19. Determine which relationship ⊆, =, ⊇ is true between each pair of sets.

a. A ∩ (A ∪ B), A ... Close

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=
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b. A ∩ (B ∪ C), (A ∪ B) ∩ (A ∪ C) ... Close

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c. A ∪ (B ∩ C), (A ∪ B) ∩ (A ∪ C) ... Close

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=
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20. Consider the following sets. Pick the correct description. What is the cardinality of each set?

 
Changed:
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a. A ∩ (A ∪ B) = A
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a. A = {x |x N ∧ (∀y,w : y,w N ∧y ≠ 1 ∧ w ≠ 1 ∧ xyw ) } ( N is the set of natural numbers) ... Close
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Prime numbers, infinite
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Changed:
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b. A ∩ (B ∪ C) = (A ∪ B) ∩ (A ∪ C)
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b. A = {x |x N ∧ x < 100 ∧ (∃y: y N ∧ x = 3y) } ( N is the set of natural numbers) ... Close
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multiples of 3 {3, 6, 9, ... 99}, 33
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  -- JimSkon - 2011-03-14 \ No newline at end of file
 
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