Let $M(x,y)$ be $"x$ has sent $y$ an e$-$mail," and $T(x,y)$ be $"x$ has sent $y$ a text

message," where the domain for $x$ and $y$ consists of all students in our class. Express

each of these sentences in terms of $M,T,$ quantifiers, and logical operators.

$($a$)$ No one in our class emailed Roberto. $($Assume Roberto is a student in the class.$)$

$($b$)$ Everybody in the class sent a text message to somebody in the class.

$($c$)$ Everybody in the class sent a text message to somebody else in the class.

$($d$)$ There is someone in the class who sent an email to everyone else in the class, or

sent a text message to everyone else in the class.