Fundamental Concepts of Sets

Set Representation

• Roster notation: $A=\{1,2,3\}$
• Set-builder notation: $B=\{x\mid x\text{ is even},1\le x\le 10\}$
• Interval notation: $C=[1,5]=\{x\mid 1\le x\le 5\}$

集合的表示

• 列举法：$A=\{1,2,3\}$
• 描述法：$B=\{x\mid x\text{ 是偶数},1\le x\le 10\}$
• 区间表示：$C=[1,5]=\{x\mid 1\le x\le 5\}$

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Set Operations

Operation	Symbol	Definition	Example
Union	$A\cup B$	$\{x\mid x\in A\text{ or }x\in B\}$	$\{1,2\}\cup \{2,3\}=\{1,2,3\}$
Intersection	$A\cap B$	$\{x\mid x\in A\text{ and }x\in B\}$	$\{1,2\}\cap \{2,3\}=\{2\}$
Difference	$A\setminus B$	$\{x\mid x\in A\text{ and }x\mathrm{\notin }B\}$	$\{1,2,3\}\setminus \{2\}=\{1,3\}$
Complement	$\bar{A}$	Elements in universal set $U$ not in $A$	If $U=\{1,2,3,4\},A=\{1,2\}$
Symmetric difference	$A\mathrm{△}B$	$(A\setminus B)\cup (B\setminus A)$	$\{1,2\}\mathrm{△}\{2,3\}=\{1,3\}$

The difference opration is \, not /