PROBLEM $4(20$ POINTS, $10$ POINTS EACH$)$

Given the below circuit. The comparator is supplied by a $+15$ V and $-15$ V DC power supply so its output will be $+15$ or $-15$ V based on inputs.

a$)$ Find the two reference voltages: $V_{\text{r}\text{e}\text{f}-\text{h}\text{i}\text{g}\text{h}}$ and $V_{\text{r}\text{e}\text{f}-\text{l}\text{o}\text{w}}?$

b$)$ Suppose that currently, the output is high $($i$.$e$.,$ at $+15$ V $),$ what is the output voltage $($stay the same at $+15$ V or change to $-15$ V $)$ if input $1$ is $470$ mV and input $2$ is $500$ mV $?$ Explain why?

Fig. $4.$ Circuit diagram for Problem $4.$