SETS_sets

SETS_sets - B ) ∪ C = ( A ∪ C ) ∩ ( B ∪ C ) Subset...

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Summary of Set Theory Set Equality A = B x x A x B A = B A B B A Subset A B x x A x B Proper Subset A B A B ∧ ¬ ( A = B ) Power Set P A = { B | B A } S P A x x S x A Set Union A B = { x | x A x B } Set Intersection A B = { x | x A x B } Set Difference A - B = { x | x A x 6∈ B } Set Complement A 0 = { x | x U x 6∈ A } Empty Set A = x x 6∈ A Universal Set A = U x x A De Morgan ( A B ) 0 = A 0 B 0 ( A B ) 0 = A 0 B 0 Commutative A B = B A A B = B A Associative ( A B ) C = A ( B C ) ( A B ) C = A ( B C ) Distributive ( A B ) C = ( A C ) ( B C ) ( A
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Unformatted text preview: B ) ∪ C = ( A ∪ C ) ∩ ( B ∪ C ) Subset Properties A ∩ B ⊆ A A ⊆ A ∪ B ∅ ⊆ A A ⊆ A A ⊆ B ∧ B ⊆ C ⇒ A ⊆ C Emptyset Identities A ∩ ∅ = ∅ A ∪ ∅ = A A- ∅ = A ∅ -A = ∅ ∅ = U Universal Set Identities A ∩ U = A A ∪ U = U A-U = ∅ U-A = A U = ∅...
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This note was uploaded on 01/19/2010 for the course CS 246 taught by Professor Wormer during the Spring '08 term at Waterloo.

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