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HMMT 二月 2004 · 团队赛 · 第 9 题

HMMT February 2004 — Team Round — Problem 9

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [15] If b is any element of T , prove that b ? b = b . Now suppose further that ( a ? b ) ? c = a ? ( b ? c ) for all a, b, c ∈ S . (Thus we can write an expression like a ? b ? c ? d without ambiguity.)
解析
  1. If b is any element of T , prove that b ? b = b . Solution: If b ∈ T , then b = a ? a for some a , so b ? b = ( a ? a ) ? ( a ? a ) = a ? a (by the given property) = b . Now suppose further that ( a ? b ) ? c = a ? ( b ? c ) for all a, b, c ∈ S . (Thus we can write an expression like a ? b ? c ? d without ambiguity.)