DLMF:26.18.E1 (Q7984)

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DLMF:26.18.E1
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    | S ( A 1 A 2 A n ) | = | S | + t = 1 n ( - 1 ) t 1 j 1 < j 2 < < j t n | A j 1 A j 2 A j t | . 𝑆 subscript 𝐴 1 subscript 𝐴 2 subscript 𝐴 𝑛 𝑆 superscript subscript 𝑡 1 𝑛 superscript 1 𝑡 subscript 1 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 𝑡 𝑛 subscript 𝐴 subscript 𝑗 1 subscript 𝐴 subscript 𝑗 2 subscript 𝐴 subscript 𝑗 𝑡 {\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|.}}
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    DLMF:26.18.E1
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    | A | 𝐴 {\displaystyle{\displaystyle\left|\NVar{A}\right|}}
    C26.S1.p2.t1.r5.m3adec
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    {\displaystyle{\displaystyle\cap}}
    introduction.Sx4.p1.t1.r27.m2adec
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    {\displaystyle{\displaystyle\setminus}}
    introduction.Sx4.p2.t1.r19.m2adec
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    {\displaystyle{\displaystyle\cup}}
    introduction.Sx4.p1.t1.r28.m2adec
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    j 𝑗 {\displaystyle{\displaystyle j}}
    C26.S1.XMD3.m1dec
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