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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 20:34, 2 February 2009
, 20:34, 2 February 2009→Definition 2
===Definition 2===
===Definition 2===
====Variant 1====
<br>
<br>
|- style="height:40px; text-align:center"
|- style="height:40px; text-align:center"
| width="80%" |
| width="80%" |
| width="20%" | <math>\text{Definition 2}\!</math>
| width="20%" | <math>\operatorname{Definition~2}</math>
|}
|}
|-
|-
| <math>x \in P ~\Leftrightarrow~ x \in Q</math>
| <math>x \in P ~\Leftrightarrow~ x \in Q</math>
| align="center" | <math>\forall x \in X</math>
| align="center" | <math>\forall x \in X</math>
|}
|}
<br>
====Variant 2====
<br>
{| 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%"
|
{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px; text-align:center"
| width="80%" |
| width="20%" | <math>\operatorname{Definition~2}</math>
|}
|-
|
{| 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>\text{If}\!</math>
| width="80%" style="border-top:1px solid black" | <math>P, Q ~\subseteq~ X</math>
|- style="height:40px"
|
| <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
|}
|-
|
{| 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="80%" style="border-top:1px solid black" | <math>P ~=~ Q</math>
|- style="height:60px"
|
| <math>\operatorname{D2b.}</math>
| <math>\overset{X}{\underset{x}{\forall}}~ (x \in P ~\Leftrightarrow~ x \in Q)</math>
|}
|}
|}
|}