Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even.

According to the Handshaking Lemma for any undirected graph $G = (V, E)$:

1. Statement Q: Since the sum equals $2|E|$, which is twice the number of edges, the sum of degrees of all vertices is always an even number. Thus, Q is TRUE.

2. Statement P: Partition the vertices into those with even degree ($V_{\text{even}}$) and odd degree ($V_{\text{odd}}$):

   $$\sum_{v \in V_{\text{even}}} \text{deg}(v) + \sum_{v \in V_{\text{odd}}} \text{deg}(v) = 2|E|$$

   Since the total sum ($2|E|$) is even and the sum of even numbers is even, the sum $\sum_{v \in V_{\text{odd}}} \text{deg}(v)$ must also be even. A sum of odd integers is even if and only if the number of terms is even. Therefore, the number of odd-degree vertices must be even. Thus, P is TRUE.

Since both statements P and Q are true, the correct option is (C).