?34E Show that when woman do the proposing in the deferred acceptance algorithm, the matching produced is female optimal and male pessimal. In Exercises 35 and 36 we consider variations on the problem of finding stable matchings of men and women described in the preamble to Exercise 61 in Section 3.1.

MODULE 14: INDUCTION AND RECURSIVE DEFINITION/ALGORITHM Induction/Recursive Definition Algorithm Chapter Summary Mathematical Induction Strong Induction Well-Ordering Recursive Definitions Structural Induction Recursive Algorithms → 5.1 Mathematical Induction ← Climbing an Infinite Ladder Suppose we have an infinite ladder: 1. We can reach the first rung of the ladder. 2. If we can reach a particular rung of the ladder, then we can reach the next rung. From (1), we can reach the first rung. Then by applying (2), we can reach the second rung. Applying (2) again, the third rung. And so on. We can apply (2) as many times as we feel to reach any particular rung no matter the height.