A NiO$-80$ mol$\%$ MgO ceramic is allowed to solidify. $($See the figure below.$)$

$($i$)$

$($a$)$ Determine the composition $($in mol$\%$MgO $)$ of the first solid to form.

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$($b$)$ Determine the composition $($in mol$\%$MgO $)$ of the last liquid to solidify under equilibrium conditions.

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