Let's analyze each option:
(1) Vectors from plasmid:
Blue-white screening is used to select recombinant bacteria, not vectors from plasmids. Hence, this is not the correct answer.
(2) Gram-positive bacteria from Gram-negative bacteria:
Blue-white screening does not differentiate between Gram-positive and Gram-negative bacteria. This is not the correct answer.
(3) Antibiotic-resistant bacteria:
While antibiotic resistance may be involved in cloning, blue-white screening is specifically used to distinguish recombinant bacteria from non-recombinant bacteria. Hence, this is not the correct answer.
(4) Recombinant bacteria from non-recombinant bacteria:
Blue-white screening is used to select recombinant bacteria (those that have successfully taken up the foreign DNA) from non-recombinant bacteria (those that have not). This is the correct answer.
Conclusion:
The correct answer is Option 4: Recombinant bacteria from non-recombinant bacteria.