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HMMT 二月 2008 · TEAM2 赛 · 第 1 题

HMMT February 2008 — TEAM2 Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 10 ] (Distributive law) Prove that ( x ⊕ y ) z = x z ⊕ y z for all x, y, z ∈ R ∪ {∞} . n
解析
  1. [ 10 ] (Distributive law) Prove that ( x ⊕ y ) z = x z ⊕ y z for all x, y, z ∈ R ∪ {∞} . Solution: This is equivalent to proving that min( x, y ) + z = min( x + z, y + z ) . Consider two cases. If x ≤ y , then LHS = x + z and RHS = x + z . If x > y , then LHS = y + z and RHS = y + z . It follows that LHS = RHS . n