Exercise 1. The following lemma is important for the base case of the induction proof of the main theorem. Prove all three claims of this lemma using Proposition 2. Lemma 7. The empty set Ø can be counted by 0. The empty set is the only set that can be counted by 0 (in other words, if a set S is counted by 0, it is empty). Furthermore, the empty set cannot be counted by n > 0.

Does there happen to be more to this solution? I still can't quite follow

A tortoise and hare are competing in a 400-meter race. The arrogant hare gives the tortoise a 220-meter head start. When the start gun is fired, the hare begins running at a constant speed of 3.5 meters per second and the tortoise begins crawling at constant speed of 1.5 meters per second. Take out a piece of paper and read the above problem context again. You will prepare your written work and solutions on your own paper and upload it and the end of this question. Complete the problem solving process by: i. reading and re-reading the problem to identify the quantities in the situation; ii. making a drawing to represent the relevant quantities in the situation; iii. and defining the variable t to represent the number of seconds since the start of the race. a. Define a function f to determine the distance of the tortoise from the finish line in terms of the number of seconds, t, since the start of the race. Preview Solve f(t) = 0 and describe what your solution represents. t = Preview…

doesn't make sense. can you please explain a bit better?