The temperature$/$composition diagram for the $C\frac{a}{S}$i binary system is shown below. You should indicate whether a liquid is Ca$-$rich or Si$-$rich.

$($a$)(3$ points, no partial credit$)$ Indicate what is A and $B$

A: Ca B: ST

$($b$)(7$ points$)$ If $0\mathrm{.}8$ mole fraction melt of $Ca$ at $1,500C$ is cooled to $1,030C,$ what phases would be at equilibrium? Estimate the relative amounts of each phase.

$($c$)$ If $0\mathrm{.}2$ mole fraction melt of $Ca$ at $1,500C$ is cooled at $1,030C.$ What phases, and relative amounts, would be at equilibrium at a temperature slightly higher than points$)$ and slightly lower than points$)?$