It it possible to express an always-true function using product of sums in boolean algebra?

Question

Consider such boolean function: $$f(x,y,z) = 1$$ It is easy, but a trifle tedious, to express this function using the sum of products. However, let's say that we are asked to express it using the product of sums.
Is this even possible?

Answer 1

A non-empty conjunctive form containing all three variables is $$f(x,y,z)=1=(x+\neg{x})(y+\neg y)(z+\neg z)$$

Answer 2

$x + \lnot x$ is both a sum of products (disjunctive normal form) and a product of sums (conjunctive normal form) for the identically true function on any number of propositional variables.