- $P:$ Bank receipt is forged
- $Q:$ Mr. $M$ is liable
- $R:$ He will go bankrupt
- $S:$ Bank loan him money
- If the bank receipt is forged, then Mr. M is liable. $P\rightarrow Q$
- If Mr. M is liable, he will go bankrupt. $Q\rightarrow R$
Now, With Hypothetical Syllogism
$P\rightarrow Q$
$Q\rightarrow R$
----------------------
$P\rightarrow R$ -----------------$(1)$
-----------------------
$3.$If the bank will loan him money, he will not go bankrupt. $S\rightarrow \sim R=\sim S\vee \sim R$-----------$(2)$
Now with Resolution
and from $(1)$ and $(2)$
$\sim P\vee R$
$\sim S\vee \sim R$
------------------------
$\sim P\vee \sim S$---------------$(3)$
-------------------------
$4.$The bank will loan him money. $S$
Now with Disjunctive Sillogism
$\sim P\vee \sim S$
$S$
--------------------------
$\sim P$
-------------------------
So, Conclusion is The bank receipt is not forged