Please translate into logical notation the following five English sentences, using the notation provided, and then give a prenex normal form of your translations. Each sentence is worth 0.8 point (0.5 for the translation and 0.3 for the prenex normal form). 5. All satellites that are brighter than no star that is closer to some satellite than to some planet are brighter than no star. (Sx: x is a star; Px: x is a planet; Lx: x is a satellite; Bxy: x is brighter than y; Cxyz: x is closer to y than to z.) Please translate into logical notation the following five English sentences, using the notation provided, and then give a prenex normal form of your translations. Each sentence is worth 0.8 point (0.5 for the translation and 0.3 for the prenex normal form). 5. All satellites that are brighter than no star that is closer to some satellite than to some planet are brighter than no star. (Sx: x is a star; Px: x is a planet; Lx: x is a satellite; Bxy: x is brighter than y; Cxyz: x is closer to y than to z.)