Problem $1.(10$ pts $=2\backslash$times $5)$ Consider the following predicates and constants.

Constants: A$,$ B

Predicates:

Above$($x$,$ y$)$: x is above y

On$($x$,$ y$)$: x is on y

Red$($x$)$: x is red

Free$($x$)$: x is free

domain of x and y: $\{$a set of boxes$\}$

Express each of the following statements using quantifiers, logical connectives, and the predicates given

above. You may use variables, other than x and y$,$ when$/$if needed.

Note$/$example: Let B be a constant. On$($x$,$ B$)$: x is on B$.$

a$)$ A is red but B is not.

b$)$ Everything is on something.

c$)$ Everything that is red is free.

d$)$ Everything that is free has nothing on it$.$

e$)$ There is something that is red and not free.