Intro2805 - SETS Set = A collection of objects E = cfw_0 2 4 P = cfw_2 3 5 7 A = cfw_A B C D Z Two sets are same if their elements are the same A =

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SETS Set = A collection of objects E = {0, 2, 4,…} P = {2, 3, 5, 7,…} A = {A, B, C, D, . . ., Z} Two sets are same if their elements are the same. A = {1,2,3} B = {2,1,3} A B: If each element of A is in B. A B: if A B and A B. A B, A B, A – B.
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SOME SPECIAL SETS : Natural Numbers : Integers : Rational Numbers : Real Numbers .
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P ROPERTIES : S ET O PERATIONS Let A, B, and C be sets. Idempotency A A = A A A =A Commutativity A B = B A A B = B A Associativity A (B C ) = (A B) C A (B C ) = (A B) C Distributivity (A B) C = (A C) (B C) (A B) C = (A C) (B C)
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Absorption (A B) A = A (A B) U A = A De Morgan’s A-(B C) = (A – B) (A- C) A-(B C) = (A – B) (A - C)
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Theorem A – (B C) = (A - B) (A- C) Proof: Let L = A - (B C). Let R =(A – B) (A – C). We show L R and R L L = R. Proof : L R Let x L. x A and x B C x B or x C x (A- B ) or x (A – C) x (A- B ) x (A – C) = R
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Proof: R L Let x R x A - B or x A – C x A and x B C x A – ( B C ) = L
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P ARTITION The partition of a set A 2 A such that 1. Each element of is non-empty . 2. Distinct members of are disjoint . 3. = A Example : A = {1,2,3,4} = { {1}, {2,4}, {3}} Example : A = N = {EVEN, ODD}
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R ELATIONS AND F UNCTIONS Cartesian Product of Two Sets A ×B = Set of all ordered pairs (a, b) such that a
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This note was uploaded on 11/30/2010 for the course SCS 2805 taught by Professor Smid during the Spring '09 term at Carleton CA.

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Intro2805 - SETS Set = A collection of objects E = cfw_0 2 4 P = cfw_2 3 5 7 A = cfw_A B C D Z Two sets are same if their elements are the same A =

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