la$.$ Prove that $(A^B{C}^D)|-(A^{B}C)||("$conjunctive rule splitting"$)$ is a sound rule$-$ofinference using a truth table.

lb$.$ Also prove $(A^B{C}^D)|||=(A^{B}C)$ using Natural Deduction.

$($Hint: it might help to use a ROI for "Implication Introduction". If you have a Horn clause, with $1$ positive literal and $n-$I negative literals, like $(notxvvZvvnotY),$ you can transform it into a conjunctive rule by collecting the negative literals as positive antecedents, e$.$g$.x^{Y}Z.$ This is a truth$-$preserving operation $($hence sound$),$ which you could prove to yourself using a truth table.$)$

$1$c$.$ Also prove $(A^B{C}^D)|||=(A^{B}C)$ using Resolution.