Assignment3_solutions

Assignment3_solutions - MACM 101 — Discrete Mathematics I...

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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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Assignment3_solutions - MACM 101 — Discrete Mathematics I...

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