handouts4_sets

# handouts4_sets - Set Theory Mariusz Bajger COMP2781/8781...

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Unformatted text preview: Set Theory Mariusz Bajger COMP2781/8781 School of Computer Science, Engineering and Mathematics April 29, 2011 1/12 Reading and Exercises Reading Epp, Chapter 6 Exercises Sec. 6.1, 6.2 and 6.3 (all in blue), 6.4 (Ex. 13- 26, in blue) Good learning strategy: BE ACTIVE! I Regularly revise lectures I Solve the suggested exercises I Be critical when reading textbook/lectures I Ask your colleagues, ask the lecturer, don’t be shy! I It is OK to ask for help any time 2/12 Operations on Sets Assume that A and B are subsets of a universal set U . This set U provides the context for discussion and its existence is critical for validity of all set theory concepts. A = B ⇔ A ⊆ B and B ⊆ A A ∪ B = { x ∈ U | x ∈ A or x ∈ B } A ∩ B = { x ∈ U | x ∈ A and x ∈ B } B \ A = { x ∈ U | x ∈ B and x / ∈ A } A c = { x ∈ U | x / ∈ A } EXAMPLE Check whether the sets A = ( − 2 , ∞ ), B = [1 , ∞ ) are equal. Find A ∩ B , A \ B , A c , B \ A , A ∪ B . 3/12 Proving set identities Prove that for any nonempty sets A and B : A \ B = A ∩ B c ....
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handouts4_sets - Set Theory Mariusz Bajger COMP2781/8781...

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