handout2 - ∩ ∪ and c and properties of AND OR and ¬ If...

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MAA4224 – Introduction to Analysis – Eriko Hironaka Handout 2 Supplement to 1.2 – Properties of sets Notation: Notice that there is often an implied meta-set containing all given sets. Usually in this class the meta-set will be the set of real numbers. x A x is an element of A” x A c x is in the complement of A (in the meta-set)” x A B x is in A and x is in B” x A B x in A or x is in B or x is in both” Laws governing intersections: A ( B C ) = ( A B ) ( A C ) A ( B C ) = ( A B ) ( A C ) De Morgan’s Laws: ( A B ) c = A c B c ( A B ) c = A c B c Notice the similarities between properties of
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Unformatted text preview: ∩ , ∪ and c , and properties of AND , OR and ¬ . If A, B, C are statements, then A AND ( B OR C ) ⇔ ( A AND B ) OR ( A AND C ) . A OR ( B AND C ) ⇔ ( A OR B ) AND ( A OR C ) . ¬ ( A AND B ) ⇔ ( ¬ A ) OR ( ¬ B ) . ¬ ( A OR B ) ⇔ ( ¬ A ) AND ( ¬ B ) . What is behind this analogy? Sometimes + and · are used to denote AND and OR . Is this justified considering the usual rules of + and · ? Try replacing AND , OR and ⇔ with +, · and = in the above equations. 1...
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