## Logic help

Course: Logic

I have the following logic problem:

You find a box that may contain a ruby, a diamond, neither, or both. Three guards make the following statements:

Aram: Clew is lying if and only if the ruby is in the box.
Bard: If exactly one of my fellow guards is lying, then the diamond is in the box.
Clew: Exactly one gemstone is in the box.

I'm converting these statement using logical operators so that I can make the truth table.

r=ruby is in the box
d=diamond is in the box

Aram: $\sim C\leftrightarrow r$ (Which I am storing as capital 'A')

Bard: $\left(A \oplus C\right)\rightarrow d$

Clew: $r\oplus d$ (Which I am storing a capital 'C')

Can someone check 3 statements that I created?