PLEASE WRITE THE QUESTION IN HAND$-$WRITTEN FORM NOT USING CALCULATOR.

We define the following propositions:

$p$ means $"$It is lunchtime", $q$ means $"$It is a working day", and $r$ means $"$It is sunny"

Also we define the following predicates:

$A(x)$ means person $x$ is hungry. $B(x)$ means the person $x$ eats at the university restaurant. $C(x)$ means $x$ goes out.

The universal ser is some set of people, that includes at least the person "Jack".

a$)$ Write the following sentence as a formula: $"$If it is sunny, then Jack will go out, and if he is out and hungry, he will eat at the university restaurant".

b$)$ Write the following sentence as a formula: $"$If it is not sunny, no one will go out on a weekday"

c$)$ Write the following sentence as a formula $"$No one eats at the university restaurant if it is not lunchtime and a working day".