ALL QUESTIONS

1.5.6. Show that in any group of at least two people there are at least two persons that have the same number of acquaintances within the group. (Use the pigeonhole principle.) 1.5.7. Suppose we try to prove, by an argument exactly parallel to the proof of Theorem 1.5.2, that the set of all finite subsets of N is uncountable. What goes wrong? 1.5.8. Give examples to show that the intersection of two countably infinite sets can be either finite or countably infinite, and that the intersection of two uncountable sets can be finite, countably infinite, or uncountable