## Problem 6### Instructions:For each of the following statements, indicate whether the statement is true or false and justify your answer with a proof or a counterexample.### Statements:#### (a)**Statement:**Let \( m \in \mathbb{N} \) and let \( a, b, c \in \mathbb{Z} \). If \( m \nmid c \) and \( ca \equiv cb \ (\text{mod}\ m) \), then \( a \equiv b \ (\text{mod}\ m) \).#### (b)**Statement:**If \( m \in \mathbb{N} \), then the only solutions of the equation \( X^2 = X \) in \( \mathbb{Z}/m\mathbb{Z} \) are \( 0_{\mathbb{Z}/m\mathbb{Z}} \) and \( 1_{\mathbb{Z}/m\mathbb{Z}} \).

Answered: Image /qna-images/answer/e4056201-efa0-46be-a239-3725a91709e7.jpg

6. For each of the following statements, indicate whether the statement is true or false and justify your answer with a proof or a counterexample. (a) Let me N and let a, b, c € Z. If mfc and ca = cb (mod m), then a = b (mod m). (b) If m € N, then the only solutions of the equation X² = X in Z/mZ are Oz/mz and 1z/mz.