Logic/Conversion, inversion and contraposition
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* [[wikipedia:Inverse_(logic)|Inverse (logic)]] | * [[wikipedia:Inverse_(logic)|Inverse (logic)]] | ||
* [[wikipedia:Contraposition|Contraposition (logic)]] | * [[wikipedia:Contraposition|Contraposition (logic)]] | ||
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| + | == Overview == | ||
| + | |||
| + | Definition of conversion, inversion and contraposition by truth table. | ||
| + | |||
| + | 0 means false, 1 means true, and ≡ means equivalent. | ||
| + | |||
| + | If "P→Q" then its conversion is "Q→P", inversion is "￢P→￢Q" and contraposition is "￢Q→￢P". | ||
| + | |||
| + | {| border="1" class="wikitable" style="text-align:center;" | ||
| + | ! P !! Q !! P→Q !! ￢P !! ￢Q !! Q→P：逆 !! ￢P→￢Q：裏 !! ￢Q→￢P：対偶 | ||
| + | |- | ||
| + | |0|| 0|| 1|| 1|| 1|| 1|| 1|| 1 | ||
| + | |- | ||
| + | |0|| 1|| 1|| 1|| 0|| 0|| 0|| 1 | ||
| + | |- | ||
| + | |1|| 0|| 0|| 0|| 1|| 1|| 1|| 0 | ||
| + | |- | ||
| + | |1|| 1|| 1|| 0|| 0|| 1|| 1|| 1 | ||
| + | |} | ||
== CAI Exercise == | == CAI Exercise == | ||
Latest revision as of 08:37, 23 May 2014
Logic > Conversion, inversion and contraposition
Contents
- Category:Mathematical logic（Wikipedia）
- Propositional calculus
- Converse (logic)
- Inverse (logic)
- Contraposition (logic)
Overview
Definition of conversion, inversion and contraposition by truth table.
0 means false, 1 means true, and ≡ means equivalent.
If "P→Q" then its conversion is "Q→P", inversion is "￢P→￢Q" and contraposition is "￢Q→￢P".
| P | Q | P→Q | ￢P | ￢Q | Q→P：逆 | ￢P→￢Q：裏 | ￢Q→￢P：対偶 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
| 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |
