Computer Science 2214A/B Study Guide - Final Guide: University Of Western Ontario, Distributive Property, Disjoint Sets

• School: Western University
• Department: Computer Science
• Course: Computer Science 2214A/B
• Professor: Lila Kari

Document Summary

The rst one is short, but requires some intuition and practice, which can be gained by drawing pictures, like the one below. The second solution is longer and less elegant; but it is also more detailed. B a c b, which implies b = a = c. The rst hypothesis, namely a b = c implies that both a and b are contained in c, that is. Now looking at the third hypothesis, namely (a c) b = a, we see that by applying distributivity of over we obtain: (a b) (c b) = a. Now using distributivity of over , we further deduce: Since c b is contained in c, we have c (c b) = c and we derive this equality: It remains to be proved that a = b holds. Using c = a within the the second hypothesis, namely (a c) b = c, we obtain: that is, (a a) b = a,