Math Problem Statement

  1. Верно ли каждое из следующих равенств

(R1∪R2)−1=R1−1∪R2−1(R1​∪R2​)−1=R1−1​∪R2−1​;

(R1∩R2)−1=R1−1∩R2−1(R1​∩R2​)−1=R1−1​∩R2−1​

для бинарных отношений R1R1​ и R2R2​, определённых на произвольном множестве MM? Ответ «да», надо обосновать, ответ «нет» аргументировать приведением примера.

Solution

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Set Theory
Binary Relations
Inverse Relations

Formulas

(R1 ∪ R2)⁻¹ = R1⁻¹ ∪ R2⁻¹
(R1 ∩ R2)⁻¹ = R1⁻¹ ∩ R2⁻¹

Theorems

Inverse of a Union of Relations
Inverse of an Intersection of Relations

Suitable Grade Level

University Level (Discrete Mathematics)