Question

f:B -> A x B, defined by f(x) = (x, b), where be is a fixed element in of B
is f bijective? if so prove it.

Answer 1

Is B a singleton?

Answer 2

If not, then there exists an element \(a \in B\) such that \(a\ne b\)

Implying the existence of the element \((a,a)\) for which there may not exist an element
\(x \in B\) such that \(f(x) = (a,a)\)