Unformatted text preview: 3. (3 points) How many 6-letter words are there whose letters appear in alphabetical order? 4. The following questions refer to relations A ⊆ V × V , where V is a set with n elements. (a) (3 points) How many diﬀerent symmetric relations are there? (The answer should be a function of n .) (b) (3 points) How many anti-symmetric relations are there? (c) (3 points) How many relations are there that are both symmetric and anti-symmetric? (d) (3 points) Prove or disprove: if A 2 = A 4 then A = A 4 . (e) (3 points) Prove or disprove: if A is total then A 2 is total. (f) (3 points) If A is symmetric then which properties does A 2 have? (Reﬂexive, symmetric, anti-symmetric, total, transitive) 5. (3 points) S ⊆ Z × Z is the relation where for x, y ∈ Z , S ( x, y ) holds if and only if y = x +2 or y =-x . Give a simple description of S * and show how you derived your answer. 1...
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- Fall '07
- Different, Discrete Mathematics Homework, discussion section number, diﬀerent symmetric relations