| Version 6 |
Version 5 |
| You can see that the contrapositive of an implication is true by considering |
You can see that the contrapositive of an implication is true by considering |
| the following: |
the following: |
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| The statement $p\Rightarrow q$ is logically equivalent to $\neg p\vee q$ which can also be written as $\overline{p}\vee q$. |
The statement $p\Rightarrow q$ is logically equivalent to $\neg p\vee q$ which can also be written as $\overline{p}\vee q$. |
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| By the same token, the contrapositive statement $\overline{q}\Rightarrow \overline{p}$ is logically equivalent to $\neg \overline{q}\vee \overline{p}$ which, using double negation on $q$, becomes $q\vee \overline{p}$. |
By the same token, the contrapositive statement $\overline{q}\Rightarrow \overline{p}$ is logically equivalent to $\neg \overline{q}\vee \overline{p}$ which, using double negation on $q$, becomes $q\vee \overline{p}$. |
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| This, of course, is the same logical statement. |
This, of course, is the same logical statement. |
