Is LCT able to solve the following problem?

Given an undirected graph $$$G=(V, E)$$$, there are three types of queries, and these queries may be asked in an arbitrary order:

(1) Add an edge $$$e$$$ to $$$E$$$. It is guaranteed that $$$e \notin E$$$ before this query.

(2) Delete an edge $$$e \in E$$$. It is guaranteed that $$$e \in E$$$ before this query.

(3) Query the number of connected components in $$$G$$$.

LCT could answer whether two arbitrary vertices $$$u, v$$$ are connected after queries of type (1, 2), but what about queries of type (3)?

I know little about LCT, I use LCT as a black box. At about ~1600 rating I seldom solve problems using LCT. This problem comes from my data mining course project: I want to dynamically maintain social cycles.