$(2)$ Construct the hypothetical binary system A$-$B which represents the following conditions

$($label all areas$)$:

a$.$ Component A melts at $1800C.$

b$.$ Component $B$ melts at $1550C.$

c$.$ Compound $A_2{B}_3$ melts congruently at $1450C.$

d$.$ Compound $A_{2}B$ melts incongruently at $1400C.$

e$.$ A maximum of $25\%$ of $B$ is soluble in $A_2{B}_3$ forming the solid$-$solution phase $.$

f$.$ A eutectic exists between $($ss$)$ and $B$ at $1300C.$

g$.-A_{2}B$ transforms to $-A_{2}B$ when heated above $1150C.$

h$.$ A eutectic exists between $-A_{2}B$ and $A_2{B}_3$ at $1300C.$