# Showing that the diagonal of $X\times X$ is transversal to the graph of $f$. (1.5.10 Guillemin and Pollack)

The question and its answer is given below:

But I am wondering, is it also correct if I showed that graph f is transversal to diagonal of $$X\times X$$?

Also, I can not understand the general idea he using in his proof in the last paragraph, could anyone explain this for me please?

EDIT:

These are the exercises referred to:

Thank you!