Can the following clause be converted to conjunctive normal form? If so how?
$$ (a \implies b) \implies (c \implies d) $$
I tried applying DeMorgans laws and am unable to get the result.
$$ (a \implies b) \implies (c \implies d) = \lnot(\lnot a \lor b) \lor (\lnot c \lor d) = (a \land \lnot b) \lor (\lnot c \lor d) $$
You made a good start but you've missed a $\lnot$ before $b$ in the last formula (EDIT: now fixed). After fixing that, use the distributivity law $(x \land y) \lor z = (x \lor z) \land (y \lor z)$ to lift the conjunction up to the top: \begin{align*} (a \implies b) \implies (c \implies d) &= \lnot(\lnot a \lor b) \lor (\lnot c \lor d) \\ &= (a \land \lnot b) \lor (\lnot c \lor d) \\ &= (a \lor \lnot c \lor d) \land (\lnot b \lor \lnot c \lor d) \end{align*}
PS: every propositional formula can be converted to conjunctive normal form.