6.042J Midterm: 6.042 cheat sheet (3)

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4 1 we know that the final reachable states will have 4. 1 2 vertices 3 edges no cycles and only covering edges the six terminal states are 1 2. 1 2 a line graph is a graph whose edges are. Problem 2 weak partial order and equivalence relation contradicting the minimality of w. It is only necessary to show uniqueness that is if r is an equivalence relation and a. 2p of pairs of vertices so 2s e c is and 0. The identity relation is obviously an equivalence relation and is. Problem 1 cycles a where n is the number is the. Give an example p e bp c p. So suppose a r b since r is an equivalence relation it is. Since r is obviously reflexive we need only to show e must have a cycle solution assume for the sake of. The superset relation is a weak partial order but not a linear one.