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lec0427 - CS 173 Discrete Mathematical Structures Cinda...

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CS 173: Discrete Mathematical Structures Cinda Heeren [email protected] Siebel Center, rm 2213 Office Hours: BY APPOINTMENT
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Cs173 - Spring 2004 CS 173 Announcements Hwk #12 available, due4/30, 8a Final Exam: 5/10, 7-10p, Siebel 1404 Email Cinda with conflict. Problem #13 available, due5/3, 8a.
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Cs173 - Spring 2004 CS173 Partially Ordered Sets (POSets) Ex. A common partial order on bit strings of length n, {0,1} n , is defined as: a 1 a 2 …a n b 1 b 2 …b n If and only if a i b i , 2200 i. 0110 and 1000 are “incomparable” … We can’t tell which is “bigger.” As a bit of an aside, this relation is exactly thesame as the last example, (2 S , ). A. 0110 1000 B. 0110 0000 C. 0110 1110 D. 0110 10111 Huh? Set S, on which webuild 2 S , has a size. That’s n. Suppose S is {a,b}. Then 2 S = { {}, {a}, {b}, {a,b} } Think of bit strings as membership indicators for the elts of S Then 2 S can be represented by {00,10,01,11}
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Cs173 - Spring 2004 CS173 Partially Ordered Sets (POSets) 0110 and 1000 are “incomparable” … We can’t tell which is “bigger.” As a bit of an aside, this relation is exactly thesame as the last example, (2 S , ). In thestring relation, wesaid 00 01 becauseevery bit in 00 is less than or = thecorresp bit in 01. String on theright has at least all the1 bits of theleft, maybemore. If each 1 represents an element in S, then right sidehas all elts of theleft, maybemore. Set S, on which webuild 2 S , has a size. That’s n. Suppose S is {a,b}. Then 2 S = { {}, {a}, {b}, {a,b} } Think of bit strings as membership indicators for the elts of S Then 2 S can be represented by {00,10,01,11}
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Cs173 - Spring 2004 CS173 Partially Ordered Sets (POSets) Let (S, ) be a PO. If a b, or b a, then a and b are comparable. Otherwise, they are incomparable.
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