(Solved): Construct formal proof of validity using the method of Conditional Proof. Assumption can be taken ...

Construct formal proof of validity using the method of Conditional Proof. Assumption can be taken only from the conclusion part. Only one assumption is allowed and clearly show where the scope of assumption ends. (Answer Must Be HANDWRITTEN) [4 marks] \( (\mathrm{x})\{(\mathrm{Fx} \cdot \mathrm{Gx}) \supset[\mathrm{Hx} v \sim(\mathrm{Ix} \vee \mathrm{J} \mathrm{x})]\} \) \[ \begin{array}{l} \sim(\exists \mathrm{x})(\mathrm{Fx} . \sim \mathrm{Gx}) \\ \sim(\exists \mathrm{x})[\mathrm{Hx} \cdot \sim(\mathrm{Ix} \cdot \sim \mathrm{Zx})] / \therefore(\mathrm{x})[\mathrm{Fx} \supset(\mathrm{Hx} \equiv \mathrm{Ix})] \end{array} \]