HMMT 二月 2004 · 团队赛 · 第 9 题
HMMT February 2004 — Team Round — Problem 9
题目详情
英文原题
- [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 anexpression like a ? b ? c ? d without ambiguity.)
解析
英文解析
- 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 anexpression like a ? b ? c ? d without ambiguity.)