(Solved): Problem 5. Define \( F: \mathbb{Z} \longrightarrow \mathbb{Z} \) and \( G: \mathbb{Z} \longrightarr ...

Problem 5. Define \( F: \mathbb{Z} \longrightarrow \mathbb{Z} \) and \( G: \mathbb{Z} \longrightarrow \mathbb{Z} \) by the rules \( F(n)=2 n \) and \( G(n)=\lfloor n / 2\rfloor \) for every integer \( n \). 1. Find \( (G \circ F)(8),(F \circ G)(8),(G \circ F)(3) \), and \( (F \circ G)(3) \). 2. Is \( G \circ F=F \circ G \) ? Explain.