Final answer:
The claim that contingencies do not contain repeated sentence letters is false, the displacement being the same regardless of following directions is generally false, and the term limits' impact on women's representation in legislature is indeterminate without specific evidence.
Step-by-step explanation:
The statement that no contingencies contain any repeated sentence letters is False. In logic, contingent statements are those that are neither necessarily true nor necessarily false. The use of sentence letters does not restrict the possibility of them being repeated within a series of propositions forming a contingency.
Regarding the statement that displacement will be the same as it would have been had he followed directions correctly can also be considered False. Displacement is a vector quantity that reflects a change in position; if directions are not followed correctly, the displacement from the initial position could differ.
Lastly, the claim that term limits have produced a statistically significant increase in the number of women serving in state legislatures cannot be validated as True or False without specific statistical evidence. Studies on this topic can show varying results, and without reviewing the specific research, it's not possible to assert its accuracy.