You are given the predicates Likes$($x$,$ y$),$ which is true if x likes y$,$ Dean$($x$),$ which is true if x is a dean, Good$($x$),$ which is true if x is good, and Professor$($x$),$ which is true if x is a professor. Since your keyboards probably do not have the special logic symbols, use these symbols to write the logic sentences in parts $($a$)$ and $($b$)$:

Symbol Meaning

$$ means

$$ means

& means

$$ means

$$ means

$=>$ means

drive$\_$spreadsheet

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$($a$)$ Translate the following sentence into first$-$order logic:

Deans are professors.

$($b$)$ Translate the following sentence into first$-$order logic:

Every good professor likes a Dean.

$($c$)(10$ points$)$ Translate the following sentence from first$-$order logic into English:

$$x Vy Dean$($x$)$ Good$($x$)$ Professor$($y$)=>$ Likes$($x$,$ y$)$

$($d$)(10$ points$)$ Translate the following sentence from first$-$order logic into English:

$$x $$y Dean$($x$)->[$Professor$($y$)-$ Good$($y$)]$