question one

Consider a party of n people. Assume That a handshake can only occur between two people. Also, assume that once two people have shaken hands they do not shake hands again. Let P(i) be the number ofhandshakes person i has taken place in. Let H be the total number of hand shakes.

Prove sigma (i=1 to n) P(i)=2h

Side note....someone in the room does not have to shake anyones hand

part 2 of this question is

Consider a party of n people with the same assumptions and notations as above. Let A={i:P(i) is odd}.

Show that |A| is even