Relations

Objects of mathematics may be related in various ways.

xample:

A set A may be said to be related to a set B if

• A is a subset of B
• A is not a subset of B
• A and B have at least one element in common

A number x may be said to be related to y if

• x < y
• x is a factor of y
• x2 + y2 = 1

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x is related to y = x R y

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Let A = {0, 1, 2} and B = {1, 2, 3}

A × B = {(a, b) ∣ a ∈ A and b ∈ B} = {(0, 1),(0, 2),(0, 3),(1, 1),(1,2 ),(1, 3),(2, 1),(2, 2),(2, 3)}

관계 = 주어진 조건에 의해 관계가 있는 원소들의 순서쌍 모두의 집합.

Example: let's say we have two sets A = {1, 2, 3} and B = {4, 5, 6, 7} and a relation R⊆A×B as:

R={(1, 5),(2, 6),(3, 5)}

• B = {4, 5, 6, 7} →co-domain, {5, 6} → image (range)

Domain: 정의역, Co-domain: 공변역(치역과 다름), image=range: 치역