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MyWikiBiz, Author Your Legacy — Thursday November 07, 2024
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{| align="center" cellpadding="2" 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%"
Corollary 1
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|- style="height:40px"
 
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| width="2%"  | &nbsp;
If X c U
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| width="18%" | &nbsp;
 
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| width="60%" | &nbsp;
and u C U,
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| align="center" style="border-left:1px solid black" width="20%" |
 
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<math>\text{Corollary 1}\!</math>
then the following statement is true:
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|- style="height:40px"
 
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| style="border-top:1px solid black" | &nbsp;
C1a. u C X  <=> {X}(u) = 1. R3a=R3c
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| style="border-top:1px solid black" | <math>\text{If}\!</math>
</pre>
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| style="border-top:1px solid black" | <math>Q \subseteq X</math>
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| style="border-left:1px solid black; border-top:1px solid black" | &nbsp;
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|- style="height:40px"
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| &nbsp;
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| <math>\text{and}\!</math>
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| <math>x \in X</math>
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| style="border-left:1px solid black" | &nbsp;
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|- style="height:40px"
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| &nbsp;
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| <math>\text{then}\!</math>
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| <math>\text{the following statement is true:}\!</math>
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| style="border-left:1px solid black" | &nbsp;
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|- style="height:40px"
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| style="border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | <math>\text{C1a.}\!</math>
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| style="border-top:1px solid black" |
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<math>x \in Q ~\Leftrightarrow~ \upharpoonleft Q \upharpoonright (x) = \underline{1}</math>
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| align="center" style="border-left:1px solid black; border-top:1px solid black" |
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<math>\text{R3a} \Leftrightarrow \text{R3c}</math>
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|}
    
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