Problem (a) Consider the following grid: O O O O O O O O O O O O) O Experiment with this activity: Color five of the points black. For each pair of black points, draw the (infinite) line that joins them. Observe that some three lines intersect in a right angle triangle. If you attempt to prove this property (that some three lines intersect in a right angle triangle), what technique will you use and why? Prove this property. (b) Redo exercise & with one additional constraint: all digits must be different (use the same Inclusion-Exclusion technique). Your answer must have the same format described in exercise 8, and this is what will be graded. (e) Prove by induction the following property for all integers n > 2: `0.5% = 0.5 - 0.57 Hint: Applying the proof by induction steps should be easy, the tricky part is how to manipulate the expression for _ 0.5' in the inductive step to get what we want