MIT6_042JS10_lec09

# MIT6_042JS10_lec09 - \$ Mathematics for Computer Science...

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lec4W.1 Albert R Meyer, Feb. 24, 2010 Mathematics for Computer Science MIT 6.042J/18.062J Partial Orders lec4W.3 Albert R Meyer, Feb. 24, 2010 {1} {1,3,5,15} {1,2} {1,3} {1,5} {1,2,5,10} {1,2,3,5,10,15,30} proper subset relation lec4W.4 Albert R Meyer, Feb. 24, 2010 means B has everything that A has and more: proper subset relation A ! B B ! A lec4W.5 Albert R Meyer, Feb. 24, 2010 properties of "# A " B implies B ! A asymmetry lec4W.6 Albert R Meyer, Feb. 24, 2010 binary relation R on set A is asymmetric : aRb implies NOT (bRa) for all a,b ! A " is asymmetric lec4W.7 Albert R Meyer, Feb. 24, 2010 properties of " # [ A " B and B " C ] implies A " C transitivity

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lec4W.8 Albert R Meyer, Feb. 24, 2010 binary relation R on set A is transitive : aRb and bRc implies aRc for all a,b,c ! A " is transitive lec4W.9 Albert R Meyer, Feb. 24, 2010 strict partial orders transitive & asymmetric lec4W.11 Albert R Meyer, Feb. 24, 2010 Subject Prerequisites subject c is a direct prerequisite for subject
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MIT6_042JS10_lec09 - \$ Mathematics for Computer Science...

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