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Unformatted text preview: R = { ( x , x ) : x 1 2 } . Now R is the identity on Y = [ , 1 2 ] , so that it is symmetric and transitive. However, R does not contain the diagonal of the big square X X , and so R is not a re F exive relation on X . For example, 1 1. 2.21 True or false with reasons. (i) The symmetric group on n letters is a set of n elements. Solution. False. (ii) If S 6 , then n = 1 for some n 1. Solution. True. (iii) If , S n , then is an abbreviation for . Solution. True. (iv) If , are cycles in S n , then = . Solution. False. (v) If , are rcycles in S n , then is an rcycle. Solution. False. (vi) If S n is an rcycle, then 1 is an rcycle for every S n . Solution. True....
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 Fall '11
 KeithCornell

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