True or False: The negation of $\sim p \Rightarrow q$ is $p \Rightarrow q$
I understand this is a simple true or false question, but I'd like to understand the underlying reason why it is true or false.
So this is my first week in a Real Analysis class and we are reviewing logic, and I know the basics. A conditional is false only when the antecedent is true and the consequence is false.
But I don't understand how to apply that logic to the above question.
So breaking down the problem if the antecedent is false and the consequence is true, that means the result is true, but since I'm negating it it is actually false; but how do I apply that to the second part of the question to determine if it is true or false?
I assume the answer is true although the antecedent and consequence are different.