Learn the WHOLE Concept, with Proof HERE:
https://youtu.be/UxUEZj_vPQo?t=3908
Theorem 1:
The cardinality of ANY Matching is less than or equal to the cardinality of ANY Vertex Cover.
Proof: Watch This.
Corollary of Theorem 1:
Size of Maximum Matching is less than or equal to the size of Minimum Vertex Cover.
Proof: Watch the above lecture.
So, the MAXIMUM matching you can create, will have size less than or equal to the size of MINIMUM Vertex Cover.
So, when can a Matching $M$ & Vertex Cover $C$ be Same??
That is possible only when $M$ is a maximum matching & $C$ is a minimum vertex cover.
So, Statement (1),(2) are correct.
Konig’s Theorem:
For a bipartite graph, the Matching number (i.e., size of a maximum matching) is equal to the vertex cover number (i.e., size of a minimum vertex cover).
https://youtu.be/UxUEZj_vPQo?t=5843
BUT this is only ONE WAY. i.e. If Matching number is same as Covering number, it doesn’t imply that the graph is Bipartite.
For counter example, Take a “complete graph K4 with one edge removed” graph, it has Matching Number 2, Vertex Covering Number 2, But it is Not bipartite.
So, Statement 3 is False.
EVERY Concept used in this question is covered, With Proof, in this lecture.
WATCH $\color{red}{\text{The COMPLETE Graph Theory Course, with ALL the Proofs, Questions, Variations}}$ etc, HERE
https://youtube.com/playlist?list=PLIPZ2_p3RNHjQoj0k-BlI9zXE0QKdl-lI
This playlist is ALL you need for ANY exam, and proper knowledge of Graph Theory.