Formula:8677

Digital Library of Mathematical Functions ID 26.18.E1

${\displaystyle{\displaystyle\left|S\setminus(A_{1}\cup A_{2}\cup\cdots\cup A_{n})\right|=\left|S\right|+\sum_{t=1}^{n}(-1)^{t}\sum_{1\leq j_{1}<j_{2}<\cdots<j_{t}\leq n}\left|A_{j_{1}}\cap A_{j_{2}}\cap\cdots\cap A_{j_{t}}\right|.}}$

Symbols List

• ${\displaystyle{\displaystyle\left|\NVar{A}\right|}}$:
• ${\displaystyle{\displaystyle\cap}}$:
• ${\displaystyle{\displaystyle\setminus}}$:
• ${\displaystyle{\displaystyle\cup}}$:
• ${\displaystyle{\displaystyle j}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle A_{k}}}$: subsets
• ${\displaystyle{\displaystyle S}}$: set
 

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