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 σ ∈ S 6 , then σ n = 1 for some n ≥ 1. Solution. True. (iii) If α, β ∈ S n , then αβ is an abbreviation for α ◦ β . Solution. True. (iv) If α, β are cycles in S n , then αβ = βα . Solution. False. (v) If σ, τ are rcycles in S n , then στ is an rcycle. Solution. False. (vi) If σ ∈ S n is an rcycle, then ασα − 1 is an rcycle for every α ∈ S n . Solution. True....
View
Full Document
 Fall '11
 KeithCornell
 Equivalence relation, Transitive relation, Symmetric relation, relation, Solution.

Click to edit the document details