HMMT 二月 2004 · 团队赛 · 第 10 题
HMMT February 2004 — Team Round — Problem 10
题目详情
- [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
- 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 .