Prove proposition is a fallacy !Fallacy Equation For the above proposition, I know it is a fallacy from the truth table when A is False and B is True. How do I prove this fallacy using natural deduction, i.e for A = and B = T, prove the above proposition as **False** OR $(( \supset ) \supset (¬ \supset ¬)) \supset $ is true

$\def\fitch#1#2{\quad\begin{array}{|l}#1\\\\\hline #2\end{array}}\def\imp{\supset}$

Indeed. The proposition is contingent; it is false when $\
eg A\wedge B$, and true otherwise.

So you must prove $\
eg A\wedge B, (A\imp B)\imp(\
eg A\imp\
eg B)\vdash \bot$.

Here is a Fitch style ND skeleton.

$$\fitch{~~1.~\
eg A\wedge B\\\~~2.~(A\imp B)\imp(\
eg A\imp \
eg B)}{~~3.~\
eg A\hspace{12ex}\wedge\mathsf E~1\quad\textsf{(Simplification)}\\\~~4.~B\hspace{13.5ex}\wedge\mathsf E~1\quad\textsf{(Simplification)}\\\\\fitch{~~5.~}{~~6.~}\\\~~7.~\\\~~8.~\\\~~9.~\
eg B\\\10.~\bot\hspace{14ex}\
eg\mathsf E~4,9\quad\textsf{(Contradiction)}}$$