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The question and its answer is given below:

enter image description here

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:

enter image description here enter image description here

Thank you!

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