Final answer:
The Supreme Court case Tinker v. Des Moines Independent Community School District concluded that wearing black armbands as a form of protest in public schools is a form of symbolic speech protected by the First Amendment, setting a significant precedent for student expression rights.
Step-by-step explanation:
The Supreme Court case that determined that wearing black armbands to protest the war is protected symbolic speech is b) Tinker v. Des Moines Independent Community School District. This landmark decision in 1969 established the principle that wearing armbands as a form of protest on public school grounds is protected by the First Amendment. Justice Abe Fortas, delivering the opinion of the 7-2 majority, stated that students do not lose their First Amendment rights to freedom of speech when they step onto school property. The students, by wearing armbands, were exercising pure speech that is entirely separate from the actions or conduct of those participating in it.
This ruling has had a lasting impact on the way First Amendment rights are interpreted in the context of public schools and student expression. The decision set a precedent that school officials must be able to show that the conduct in question would "materially and substantially interfere" with the operation of the school to justify suppressing such speech. In the case of Tinker v. Des Moines, the school's fear of disruption did not meet this substantial interference threshold.