MyWikiBiz, Author Your Legacy — Monday January 06, 2025
Jump to navigationJump to search
1,196 bytes added
, 04:22, 3 February 2009
Line 754: |
Line 754: |
| <br> | | <br> |
| | | |
− | <pre> | + | {| 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 7 | + | | |
| + | {| align="center" cellpadding="0" cellspacing="0" width="100%" |
| + | |- style="height:40px; text-align:center" |
| + | | width="80%" | |
| + | | width="20%" | <math>\operatorname{Definition~7}</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>s, t ~\text{are sentences about things in the universe}~ 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{D7a.}</math> |
| + | | width="80%" style="border-top:1px solid black" | <math>s ~\Leftrightarrow~ t</math> |
| + | |- style="height:40px" |
| + | | |
| + | | <math>\operatorname{D7b.}</math> |
| + | | <math>\downharpoonleft s \downharpoonright ~=~ \downharpoonleft t \downharpoonright</math> |
| + | |} |
| + | |} |
| | | |
− | If S, T are sentences
| + | <br> |
− | about things in the universe U,
| |
− | | |
− | then the following are equivalent:
| |
− | | |
− | D7a. S <=> T.
| |
− | | |
− | D7b. [S] = [T].
| |
| | | |
| + | <pre> |
| Rule 5 | | Rule 5 |
| If X, Y c U, | | If X, Y c U, |