Formalize the following argument using propositional language. Determine whether the argu$-$ ment is valid and explain your answer.

If both Perry and Elina admit to eating ice$-$cream, then neither of them will be grounded. But if either of them admits to eating ice$-$cream while the other doesn$$t$,$ she will be grounded while the other won$$t$.$ So unless both don$$t admit the deed, it cannot happen that both are grounded.