MathDB

Sets of irrational and rational numbers

Source: Romanian District Olympiad 2006, Grade 10, Problem 4

March 11, 2006

quadraticsabstract algebravectorgroup theoryalgebra proposedalgebra

Problem Statement

a) Find two sets

X,Y

such that

X\cap Y =\emptyset

X\cup Y = \mathbb Q^{\star}_{+}

and

Y = \{a\cdot b \mid a,b \in X \}

. b) Find two sets

U,V

such that

U\cap V =\emptyset

U\cup V = \mathbb R

and

V = \{x+y \mid x,y \in U \}