返回题库

HMMT 二月 2004 · 团队赛 · 第 10 题

HMMT February 2004 — Team Round — Problem 10

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [25] Let a be an element of T . Let the image of a be the set of all elements of T thatcan be represented as a ? b for some b ∈ T . Prove that if c is in the image of a , thena ? c = c .
解析

英文解析

  1. Let a be an element of T . Let the image of a be the set of all elements of T that can berepresented 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 .