EmberJS: Questionnaire:bind 2 checkboxes to same value, one of them Inverted

im trying to implement a simple questionnaire component in EmberJS consisting of 10 different questions, where each additional question depends on the answer of the question before(maximum depth is 6) and appears after answering that. All of those questions are yes or no questions.

What i want now is 2 checkboxes/buttons, one representing yes, one representing no.

I know i could achieve that by having 2 computed properties for each question bound to the checkboxes and setting each other(even there im not quite sure,because of the opposite binding, how to make certain none of those is true by default, resulting in the next question being shown ), but i cant help but think that having 20 computed properties for this use case isnt the best way to do things

Any better and cleaner ideas for this problem are much appreciated!