Wrong.
"We have held from the beginning and uniformly that the Due Process Clause of the Fourteenth Amendment does not apply to the States any of the provisions of the first eight amendments as such. The relevant historical materials have been canvassed by this Court and by legal scholars. These materials demonstrate conclusively that Congress and the members of the legislatures of the ratifying States did not contemplate that the Fourteenth Amendment was a short-hand incorporation of the first eight amendments making them applicable as explicit restrictions upon the States." -- U.S. Supreme Court BARTKUS v. ILLINOIS, 359 U.S. 121 (1959)
Correct. The 14th amendment does not confer any new responsibility upon the states in regard to the bill of rights. The states were already obligated to refrain from infringing upon rights reserved to the people as the tenth amendment states explicitly.