Five pirates of different ages have a treasure of 100 gold coins.On their ship, they decide to split the coins using this scheme:The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it.If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain.As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard.Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, what will happen?

Tasks

1. Summaries the above puzzle into four statements.

2. Translate the statements into formulas using symbolic logic statements

3. construct the truth table of you statements.

4. prove if the statements can be considered as tautology or not.

5. Write the negation of the statements.