Question: 1. Write the negation of For all integers x and y, the number (x - y)/s is an integer. (Don't say, "It's not true that . . . .")
2. A robot can only walk forward. Each step it takes is of length 1 foot or 2 feet. So for example, the robot may walk 6 feet by taking 4 steps as lengths 2, 2, 1, 1 or as lengths 1, 2, 1, 2. The sequence rn is defined as the number of ways the robot can walk n feet. What are r1, r2, r3, r4? Find a recurrence relation for rn. Give a combinatorial explanation for why this is the correct recurrence relation.