Assignment:
A jury composed of seven members is called upon to find an accused individual either guilty or innocent. Debbie is the jury forewoman, with Bobby and Jack appointed vice-foremen. The jury includes four more jurors, in addition to Debbie, Bobby and Jack. For each of the following cases, describe the set of all decisive coalitions for “guilty” over “innocent,” and the set of all minimal decisive coalitions for this pair of alternatives.
(a) The accused is found guilty only if all the jurors unanimously agree that he is guilty.
(b) The accused is found guilty if a majority of jurors declare him to be guilty.
(c) The accused is found guilty if at least four jurors, including Debbie, declare him to be guilty
(d) The accused is found guilty if at least four jurors, including Debbie, declare him to be guilty, or if at least five jurors, including Bobby and Jack, declare him to be guilty.
(e) The accused is found guilty if at least four jurors declare him to be guilty, or if Debbie, Bobby, and Jack declare him to be guilty.
(f) The accused is found guilty if at least five jurors, including Debbie and at leastone of her vice-foremen, declare him to be guilty.
Provide complete and step by step solution for the question and show calculations and use formulas.