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Unformatted text preview: MACM 101 — Discrete Mathematics I Exercises on Functions and Relations. Due: Tuesday, October 27th (at the beginning of the class) Reminder: the work you submit must be your own. Any collabora tion and consulting outside resourses must be explicitely mentioned on your submission. Please, use a pen. 30 points will be taken off for pencil written work. Please, write your name clearly, the way it is entered in the Grade book. Make you TA happy. 1. Using laws of set theory show that ( A B ) C = ( A C ) ( B C ) Solution From right to left: ( A C ) ( B C ) = by definition of “ ” ( A ∩ C ) ∩ ( B ∩ C ) = by De Morgan’s laws and complementation law ( A ∩ C ) ∩ C ) ∩ ( B ∪ C ) = by distributivity ( A ∩ C ∩ B ) ∪ ( A ∩ C ∩ C ) = ( definition of , complement law, domination law and commutativ ity ( A B ) C 2. Let A , B , and C be sets. Show that ( A C ) ∩ ( C B ) = ∅ Draw Venn diagrams for the expression on the left side....
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 Spring '09
 jcliu
 Math, Set Theory, Equivalence relation, Binary relation, Transitive relation

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