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Revision as of 20:15, 2 February 2009
, 20:15, 2 February 2009→Syntactic Transformation Rules: format definition box
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{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
Definition 2
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
If X, Y c U,
|- style="height:40px; text-align:center"
| width="80%" |
then the following are equivalent:
| width="20%" | <math>\text{Definition 2}\!</math>
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D2a. X = Y.
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D2b. u C X <=> u C Y, for all u C U.
{| align="center" cellpadding="0" cellspacing="0" width="100%"
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|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="80%" style="border-top:1px solid black" | <math>P, Q ~\subseteq~ X</math>
|- style="height:40px"
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| <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
|}
|-
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\operatorname{D2a.}</math>
| width="60%" style="border-top:1px solid black" | <math>P ~=~ Q</math>
| width="20%" style="border-top:1px solid black" |
|- style="height:40px"
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| <math>\operatorname{D2b.}</math>
| <math>x \in P ~\Leftrightarrow~ x \in Q</math>
| align="center" | <math>\forall x \in X</math>
|}
|}
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