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HMMT 二月 2004 · 团队赛 · 第 8 题

HMMT February 2004 — Team Round — Problem 8

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [20] Prove that a ? b = b ? a for all a, b ∈ S .
    Let T be the set of elements of the form a ? a for a ∈ S .
解析

英文解析

  1. Prove that a ? b = b ? a for all a, b ∈ S .
    Solution: We have a ? b = ( b ? a ) ? ( b ? a ) = ([ a ? b ] ? [ a ? b ]) ? ([ a ? b ] ? [ a ? b ]) = [ a ? b ] ? [ a ? b ] = b ? a.
    Let T be the set of elements of the form a ? a for a ∈ S .3