On my lecture note it was written that "Finding a clique of size $k$ in a graph is NP".
Later in an example for reduction the following was written:
"Assume we know how to answer "Is there a clique of size $k$ in a graph", then each time we will hide one node of the graph an on the newly created graph we will check Is there a clique of size $k$ in a graph:
If there is a clique of size $k$ and the node is not a part of the clique
If there is no clique of size $k$ and the node is part of the clique
I have read more about it, and wanted to be sure I have understand this example.
Given a graph, answering the question whereas or not it has clique of size $k$ is NP
Given a graph, printing a clique of size $k$ is P
If it is correct then this is an example why NP is a problem (1) that the verifier (2) is P?