Changes

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The ''relative complement'' of <math>X\!</math> in <math>Y,\!</math> for two sets <math>X, Y \subseteq U,</math> written as <math>^{\backprime\backprime} \, Y\!-\!X \, ^{\prime\prime},</math> is the set of elements in <math>Y\!</math> that are not in <math>X,\!</math> that is:

The ''relative complement'' of <math>P\!</math> in <math>Q,\!</math> for two sets <math>P, Q \subseteq X,</math> is denoted by <math>^{\backprime\backprime} \, Q\!-\!P \, ^{\prime\prime}</math> and defined as the set of elements in <math>Q\!</math> that do not belong to <math>P,\!</math> that is:

{| align="center" cellpadding="8" width="90%"

{| align="center" cellpadding="8" width="90%"

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<math>\begin{array}{lll}

<math>\begin{array}{lll}

Y\!-\!X

Q\!-\!P

& = &

& = &

\{ \, u \in U : u \in Y\ \operatorname{and}\ \underline{(} u \in X \underline{)} \, \}.

\{ \, x \in X : x \in Q ~\operatorname{and}~ \underline{(} x \in P \underline{)} \, \}.

\\

\\

\end{array}</math>

\end{array}</math>

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The ''intersection'' of <math>X\!</math> and <math>Y,\!</math> for two sets <math>X, Y \subseteq U,</math> is denoted by <math>^{\backprime\backprime} \, X \cap Y \, ^{\prime\prime},</math> and defined as the set of elements in <math>U\!</math> that belong to both of <math>X\!</math> and <math>Y.\!</math>

The ''intersection'' of <math>P\!</math> and <math>Q,\!</math> for two sets <math>P, Q \subseteq X,</math> is denoted by <math>^{\backprime\backprime} \, P \cap Q \, ^{\prime\prime}</math> and defined as the set of elements in <math>X\!</math> that belong to both <math>P\!</math> and <math>Q.\!</math>

{| align="center" cellpadding="8" width="90%"

{| align="center" cellpadding="8" width="90%"

|

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<math>\begin{array}{lll}

<math>\begin{array}{lll}

X \cap Y

P \cap Q

& = &

& = &

\{ \, u \in U : u \in X\ \operatorname{and}\ u \in Y \, \}.

\{ \, x \in X : x \in P ~\operatorname{and}~ x \in Q \, \}.

\\

\\

\end{array}</math>

\end{array}</math>