Pairing Cohomology with Homology on pg.510 in "Modern classical homotopy theory".

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Here is the paragraph in the book:

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My questions are:

1- I do not understand why if $\alpha \in \widetilde{H}_{n}(X; B),$ then it should be represented by the given map below. Could anyone explain this to me, please?

2-Is the function defined in the last line above is what is called Cap product?