The correct answer is A. Only assumption I is implicit.
The statement “Private property, trespassers will be prosecuted” is a warning to people not to trespass on the property. The warning is intended to deter people from trespassing, and it is likely that some people will read the warning and decide not to trespass. However, it is also possible that some people will not read the warning, or that they will read it and decide to trespass anyway. The statement does not provide any information about whether or not people are scared of prosecution, so assumption II is not implicit.
Assumption I is implicit because the statement is a warning. A warning is intended to deter people from doing something, and it is likely that some people will be deterred by the warning. However, it is also possible that some people will not be deterred by the warning, or that they will decide to do the thing that is being warned against anyway. The statement does not provide any information about whether or not people will be deterred by the warning, so assumption I is only implicit.