Translation of an argument in logical notation.

Question

I have to formulate the following argument into logical notation :

All accused are guilty.All who are convicted will hang.Therefore if all who are guilty are convicted then all the accused will hang.

Which I translated like this :

The premises are :

($\forall x)(Ax \rightarrow Gx)$.

($\forall x)(Cx \rightarrow Hx)$.

The conclusion is:

($\forall x)(Gx \rightarrow Cx) \rightarrow ((\forall y)(Ay \rightarrow Hy))$.

Is it a right translation ? Thank you.

Answer 1

Yes, it seems okay to me. ${}{}{}$