Problem Set 2 - Set Theory (Applied Mathematical Methods to Economics - Summer Course)

PROBLEM SET 2 – PART 2 – SET THEORY 

Exercises from Corbae, Stinchcombe, and Zeman (2009) – odd ones

Exercise 2.2.5 (Notation and Other Basics)

Exercise 2.2.7 (Notation and Other Basics)

Exercise 2.2.13 (Products, Relations, Correspondences, and Functions)

Exercise 2.5.3 (Optimal Choice for Finite Sets)

Exercise 2.5.7 (Optimal Choice for Finite Sets)

Exercise 2.6.3 (Direct and Inverse Images, Compositions)

Exercise 2.6.5 (Direct and Inverse Images, Compositions)

Exercise 2.6.11 (Direct and Inverse Images, Compositions)

Exercise 2.6.19 (Direct and Inverse Images, Compositions)

Exercise 2.6.27 (Direct and Inverse Images, Compositions)

Exercise 2.7.9 (Weak and Partial Orders, Lattices)

Exercise 2.7.15 (Weak and Partial Orders, Lattices)

Exercise 2.8.3 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.8.11 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.8.13 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.8.15 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.8.19 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.8.21 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.9.3 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.9.15 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.9.19 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.9.23 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.9.27 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.9.29 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.10.3 (Finite and Infinte Sets)

Exercise 2.10.11 (Finite and Infinte Sets)

Exercise 2.10.13 (Finite and Infinte Sets)

Exercise 2.10.17 (Finite and Infinte Sets)

Exercise 2.12.7 (Revealed Preference and Rationalizability)

Exercise 2.13.2 (Superstructures)

Exercise 2.15.1 (End-Chapter Problems)

Exercise 2.15.3 (End-Chapter Problems)