Final answer:
The statement is false; Brown v. Board of Education overturned Plessy v. Ferguson's 'separate but equal' doctrine in 1954, ruling that segregated schools were inherently unequal and unconstitutional.
Step-by-step explanation:
The statement in the question is false. Brown v. Board of Education did not establish the "separate but equal" doctrine; rather, it overturned it. Plessy v. Ferguson was the case that established "separate but equal" as a doctrine in 1896, which legitimized racial segregation until it was overturned by the landmark Supreme Court decision in Brown v. Board of Education in 1954. In Brown v. Board of Education, the Court unanimously ruled that separate educational facilities are inherently unequal, violating the Equal Protection Clause of the Fourteenth Amendment.
This decision marked a pivotal moment in the Civil Rights Movement, challenging the institutionalized racial segregation prevailing in public education at the time and setting a precedent for equal education in the United States.