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math 311w homework10

# math 311w homework10 - a,b,c We deﬁne an operation using...

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Homework 10. Due Monday, April 19, 2010 Problem 1. Find if a permutation is even or odd. a ) ± 1 2 3 4 5 6 7 8 9 10 7 5 6 9 10 2 1 4 8 3 ² b ) ± 1 2 3 4 5 6 7 8 9 3 5 2 9 1 7 4 8 6 ² Problem 2. Find the order of π . For what x Z it is true that π x = id if a ) π = ± 1 2 3 4 5 6 7 8 9 10 7 5 6 9 10 2 1 4 8 3 ² b ) π = ± 1 2 3 4 5 6 7 8 9 3 5 2 9 1 7 4 8 6 ² Problem 3. Use the deﬁnition given in class (with Δ) to prove that (12) S n is an odd permutation. Problem 4. Let a set S consist from three elements,

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Unformatted text preview: { a,b,c } . We deﬁne an operation using the following table: a b c- - - - -- - - - -- - - - - -- - - - - - - -a b a c b a c b c c b a a) Is this operation commutative?Explain your answer. b) Is this operation associative?Explain your answer. 1 Problem 5. Check if the following operations are associative: a) a * b = 2 ab b) a * b = ab + 5 c) a * b = a + b + ab 2...
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math 311w homework10 - a,b,c We deﬁne an operation using...

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