Indicate which of the following are true and which are false:

A$)$ all x are an element of Z$,$ there exists a y is an element of R$-\{0\}$ such that xy$<1.$

B$)$ all x are an element of R$*,$ all y are an element of Z such that xy$<1$

C$)$ all x are an element of R$*,$ there exists a y is an element of R such that xy $=1$