Can "an act of protest" and "a sign of protest" be used interchangeably? Are there contexts where one of these phrases should be used, and not the other?
Also, are "act of protest" and "sign of protest", idioms? Are they synonymous to each other?
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I don't think so. The semantics are straight-forward here. An act of protest might be a riot or a march; a sign of protest might be a piece of political graffiti on a wall. The one is an act, or action; the other is a signifier or symbol. In many cases either expression may fit, given the context, but the meanings are not the same.