I don't think I am right to say:
If I know $F_1$ and $\neg F_1$ then I know $F_2$?
Cos $F_1$ is not related to $F_2$? Or perhaps there's a typo? It says in my notes: negation elimination
I don't think I am right to say:
If I know $F_1$ and $\neg F_1$ then I know $F_2$?
Cos $F_1$ is not related to $F_2$? Or perhaps there's a typo? It says in my notes: negation elimination
The theorem states: From a contradiction, anything follows.
From a contradiction, anything follows. Here's proof:
$F1 \wedge \neg F1$ (Premise)
$\neg F2$ (Premise)
$F1$ (1)
$\neg F1$ (1)
$F1 \wedge \neg F1$ (3, 4)
$\neg \neg F2$ (Conclusion, 2)
$F2$ (Remove $\neg \neg$, 6)
$F1 \wedge \neg F1 \rightarrow F2$ (Conclusion, 1)
Alternatively, you can use a truth table to prove that $F1 \wedge \neg F1 \rightarrow F2$ is a tautology. Truth table generator at: http://mathdl.maa.org/images/upload_library/47/mcclung/index.html