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HMMT 二月 2004 · 团队赛 · 第 10 题

HMMT February 2004 — Team Round — Problem 10

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [25] Let a be an element of T . Let the image of a be the set of all elements of T that can be represented as a ? b for some b ∈ T . Prove that if c is in the image of a , then a ? c = c .
解析
  1. Let a be an element of T . Let the image of a be the set of all elements of T that can be represented as a ? b for some b ∈ T . Prove that if c is in the image of a , then a ? c = c . Solution: Write c = a ? b , and then a ? c = a ? a ? b = a ? b (since a ? a = a ) = c .