My work mates and I are arguing about this term since none of us can comprehend its exact definition. Can I use the expression "I have been struggling vehemently to get this email sent since last month!" with validity?
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The core meaning of vehement is ‘intense, severe’, so, yes, you can use the adverb vehemently to describe the way in which you have been struggling. However, its use is mostly restricted to describing speech, so don’t be surprised if people question its use in other contexts.
Struggle is a verb, vehemently is an adverb, so they may go together cohesively.