If $$X_n\rightarrow 3$$ in probability, then $$|X_n|\rightarrow 3 $$in probability.
If $$|X_n|\rightarrow 3 $$ in probability, then $$X_n\rightarrow 3$$ in probability.
I don't think counterexamples exist for these two statements, does that make them both true?
The first statement is true. As for the second statement, consider $X_n=3$ with probability 1/2, and $X_n=-3$ with probability 1/2. Then it is not true that $X_n\to 3$ in probability.