Question

Prove that 1. AU(BUC)=(AUB)UC​

Answer 1

Solution:-

$\rm \: let \: \: x \in \: A \cup(B \: \cup \: C)$

$\rm\Longrightarrow \: x \in \: A \: or \: x \in \: B \: \cup \: C$

$\rm\Longrightarrow \: x \in \: A \: or \: (x \in \: B \: or \: x \in \: C)$

$\rm\Longrightarrow \: (x \in \: A \: or \: x \in \: B) \: or \: x \: \in \: C$

$\rm\Longrightarrow \: x \in \: A \: \cup \: B \: \: or \: x \in \: C$

$\rm \: \Longrightarrow \: x \in \: (A \cup \: B) \cup \: C$

$\rm \therefore \: x \in \: A \cup(B \cup \: C)$

$\rm \: \Longrightarrow \: x \in \: (A \cup \: B) \cup \: C$

$\sf \: hence \: proved$

$\rm \: A \cup(B \cup \: C) = (A \cup \: B) \cup \: C$

Introduction of Set

=> The concept of set is fundamental in modern mathematics. Today this concept is being used in different branches of mathematics and widely used in the foundation of relation. the theory of sets was developed by german mathematician Georg cantor (1845 - 1918)