Is your a subject or object pronoun?

Read the excerpt from a supporting opinion of the supreme court’s ruling in plessy v. ferguson, 1896. laws permitting, and even requiring, their separation in places where they are liable to be brought into contact do not necessarily imply the inferiority of either race to the other, and have been generally, if not universally, recognized as within the competency of the state legislatures in the exercise of their police power. how does this relate to the premises of brown v. board of education? the brown case addresses whether state legislatures are equipped to judge the quality of education offered at segregated schools. the brown case addresses whether authorities believe that one race is inferior to another when creating public schools. the brown case addresses whether these laws inherently deny certain citizens equal protection under the law. the brown case addresses the legality of using police power to monitor public places separated by race.