Answer true or false to whether reach of the following statements is implication of Arrow's theorem. Argue your answer briefly in each case.

1. (a)Under no circumstances there is a social preference ordering which we could sensibly call the public interest.
2. (b)Consider the aggregation procedure by pairwise majority rule. Now consider some particular society made up of individuals with preferences over some set of alternatives. For that society majority rule violates at least one of transitivity, unanimity or independence of irrelevant alternatives.
3. (c)Consider some arbitrary aggregation procedure that is not dictatorship. You can display a society (a collection of individuals with preferences over alternatives) such that the aggregation procedure violates one of transitivity, unanimity or independence of irrelevant alternatives