3-SAT with negative-literals in each clause Does a 3-SAT problem, where in each clause there is at least a negative-literal, always has a solution?

After looking at it, seems to me that the answer is yes, but maybe there is something I am not seeing.
Consider the all-zeroes assignment, $x_1=x_2=\cdots=x_n=0$.

What if all clauses have a positive literal?