Intro to Analysis in-class_Part_4

# Intro to Analysis in-class_Part_4 - Question 2(a Use the...

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0.2 Logic and inference 13 0.2.1 Set operations and logical connectives. intersection: A B = { x . . . x A and x B } union: A B = { x . . . x A or x B } complement: A c = { x . . . x / A } diﬀerence: A \ B = { x . . . x A and x / B } = A B c product: A × B = { ( x,y ) . . . x A and y B } containment: A B ⇐⇒ ( x A = x B ) Example 0.2.7. “Convergent sequences are bounded.” ( { a n } is convergent) = ( { a n } is bounded) The set of convergent sequences is a subset of the bounded sequences.

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Unformatted text preview: Question 2. (a) Use the DeMorgan laws to argue that ( A ∩ B ) c = A c ∪ B c and ( A ∪ B ) c = A c ∩ B c . (b) Prove that the empty set is a subset of every set. 14 Math 413 Pre-preliminaries...
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## This note was uploaded on 11/26/2011 for the course MAT 4944 taught by Professor Wong during the Fall '11 term at FSU.

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Intro to Analysis in-class_Part_4 - Question 2(a Use the...

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