The following question was given to Chatgpt. Determine whats correct, fix all the mistakes, and assign a Letter grade: A$,$B$,$C$,$D$,$F $?$

Let's go through the problem as detailed in the image and relate it to our earlier discussion.### FOL Statement$\backslash [\backslash$alpha $=\backslash$exists x $($Q$($a$,$ x$)\backslash$rightarrow P$($x$,$ a$))\backslash ]$This statement asserts that there exists some $\backslash ($ x $\backslash )$ in the domain such that if $\backslash ($ Q$($a$,$ x$)\backslash )$ is true, then $\backslash ($ P$($x$,$ a$)\backslash )$ must also be true.### Interpretation $\backslash ($ I$\_1\backslash )($where $\backslash (\backslash$alpha$\backslash )$ is true$)1.**$Domain $\backslash (\backslash$mathcal$\{$D$\}\backslash )**$: $\backslash (\backslash \{$d$\_1,$ d$\_2\backslash \}\backslash )2.**$Interpretation $\backslash ($ I$\_1\backslash )**$: $-\backslash ($a$\backslash )$ refers to $\backslash ($d$\_1\backslash )-**$Predicate $\backslash ($Q$\backslash )**$: $-\backslash ($Q$($d$\_1,$ d$\_1)\backslash )$ is true $-\backslash ($Q$($d$\_1,$ d$\_2)\backslash )$ is false $-**$Predicate $\backslash ($P$\backslash )**$: $-\backslash ($P$($d$\_1,$ d$\_1)\backslash )$ is true $-\backslash ($P$($d$\_2,$ d$\_1)\backslash )$ is irrelevant since $\backslash ($Q$($d$\_1,$ d$\_2)\backslash )$ is falseUnder this interpretation:$-\backslash (\backslash$exists x $($Q$($a$,$ x$)\backslash$rightarrow P$($x$,$ a$))\backslash )$ holds because we can choose $\backslash ($ x $=$ d$\_1\backslash ).$ For $\backslash ($ x $=$ d$\_1\backslash )$: $-\backslash ($Q$($d$\_1,$ d$\_1)\backslash$rightarrow P$($d$\_1,$ d$\_1)\backslash )$ is true because $\backslash ($Q$($d$\_1,$ d$\_1)\backslash )$ is true and $\backslash ($P$($d$\_1,$ d$\_1)\backslash )$ is true.Therefore, $\backslash (\backslash$alpha$\backslash )$ is true $\backslash ($ I$\_1(\backslash$alpha$)=$ T $\backslash )$ under this interpretation.### Interpretation $\backslash ($ I$\_2\backslash )($where $\backslash (\backslash$alpha$\backslash )$ is false$)1.**$Domain $\backslash (\backslash$mathcal$\{$D$\}\backslash )**$: $\backslash (\backslash \{$d$\_1,$ d$\_2\backslash \}\backslash )2.**$Interpretation $\backslash ($ I$\_2\backslash )**$: $-\backslash ($a$\backslash )$ refers to $\backslash ($d$\_1\backslash )-**$Predicate $\backslash ($Q$\backslash )**$: $-\backslash ($Q$($d$\_1,$ d$\_1)\backslash )$ is true $-\backslash ($Q$($d$\_1,$ d$\_2)\backslash )$ is false $-**$Predicate $\backslash ($P$\backslash )**$: $-\backslash ($P$($d$\_1,$ d$\_1)\backslash )$ is false $-\backslash ($P$($d$\_2,$ d$\_1)\backslash )$ is irrelevant since $\backslash ($Q$($d$\_1,$ d$\_2)\backslash )$ is falseUnder this interpretation:$-\backslash (\backslash$exists x $($Q$($a$,$ x$)\backslash$rightarrow P$($x$,$ a$))\backslash )$ does not hold because for $\backslash ($ x $=$ d$\_1\backslash )$: $-\backslash ($Q$($d$\_1,$ d$\_1)\backslash$rightarrow P$($d$\_1,$ d$\_1)\backslash )$ is false because $\backslash ($Q$($d$\_1,$ d$\_1)\backslash )$ is true and $\backslash ($P$($d$\_1,$ d$\_1)\backslash )$ is false.Therefore, $\backslash (\backslash$alpha$\backslash )$ is false $\backslash ($ I$\_2(\backslash$alpha$)=$ F $\backslash )$ under this interpretation.### Summary$-**$Interpretation $\backslash ($ I$\_1\backslash )**$: $-$ Domain $\backslash (\backslash$mathcal$\{$D$\}=\backslash \{$d$\_1,$ d$\_2\backslash \}\backslash )-\backslash ($a$\backslash )$ refers to $\backslash ($d$\_1\backslash )-\backslash ($Q$($d$\_1,$ d$\_1)=\backslash$text$\{$true$\},$ Q$($d$\_1,$ d$\_2)=\backslash$text$\{$false$\}\backslash )-\backslash ($P$($d$\_1,$ d$\_1)=\backslash$text$\{$true$\},$ P$($d$\_2,$ d$\_1)=\backslash$text$\{$irrelevant$\}\backslash )-\backslash (\backslash$alpha$\backslash )$ is true $\backslash ($ I$\_1(\backslash$alpha$)=$ T $\backslash )-**$Interpretation $\backslash ($ I$\_2\backslash )**$: $-$ Domain $\backslash (\backslash$mathcal$\{$D$\}=\backslash \{$d$\_1,$ d$\_2\backslash \}\backslash )-\backslash ($a$\backslash )$ refers to $\backslash ($d$\_1\backslash )-\backslash ($Q$($d$\_1,$ d$\_1)=\backslash$text$\{$true$\},$ Q$($d$\_1,$ d$\_2)=\backslash$text$\{$false$\}\backslash )-\backslash ($P$($d$\_1,$ d$\_1)=\backslash$text$\{$false$\},$ P$($d$\_2,$ d$\_1)=\backslash$text$\{$irrelevant$\}\backslash )-\backslash (\backslash$alpha$\backslash )$ is false $\backslash ($ I$\_2(\backslash$alpha$)=$ F $\backslash )$This breakdown aligns with the provided interpretations and demonstrates the differing truth values of $\backslash (\backslash$alpha$\backslash )$ under different interpretations.