Problem 4. (20 points) Lines in a plane are said to be in a general position if no 2 are parallel and no 3 meet in a point. If 10 lines are drawn in general position in the plane, into how many regions do they divide the plane? Figure 2: No parallel lines. No 3 lines meet in a point Explain clearly how you found the solution. Hints and suggestions It would be a nightmare to draw 10 lines in a plane and try to count the number of regions. The problem is implicitly asking you to carry out an inductive investigation. Start by drawing 1, 2, 3, 4 lines and count the number of regions created by the lines. You may be able to spot an emerging pattern. Is there a recurrence relation that can be extracted from the pattern? Can you conjecture a formula for the number of regions created by n lines in a plane