Which amendment declared that all persons born in the U.S. are citizens and entitled to equal protection?

The 14th Amendment is the correct choice as it specifically addresses citizenship and equal protection under the law. Ratified in 1868, the amendment states that all persons born or naturalized in the United States are citizens, thereby granting them the rights and protections afforded by the Constitution. It also includes the Equal Protection Clause, which ensures that states cannot deny any person within their jurisdiction the equal protection of the laws. This was a significant advancement in civil rights, aimed at securing the rights of newly freed slaves after the Civil War.

The other options do not fulfill the same role as the 14th Amendment. The 13th Amendment, for instance, abolished slavery and involuntary servitude, but it does not provide citizenship or equal protection. The 15th Amendment addresses voting rights but does not concern citizenship or equal protection directly. The Civil Rights Bill of 1866 was a precursor to the 14th Amendment and aimed to protect the rights of African Americans, but it didn't have the constitutional weight and permanence that the 14th Amendment provides. Thus, the 14th Amendment stands as a key piece of legislation in defining citizenship and protecting the rights of individuals in the U.S.