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Hello I have a question about support vector machine in my data analysis course.

I am given the following statement:

a SVM soft margin classifier with the cost parameter C > 0 to a data set that is linearly separable then resulting decision boundary is guaranteed to separate the classes.

I need to Prove or disprove the claim, and I am pretty sure it is correct but I am lost in trying to figure out how to prove it. any idea or direction will be highly appreciated

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