Which of the following statements about electric charge is true?

Option (1) states: "The charge gained by the uncharged body from a charged body due to conduction is equal to half of the total charge initially present."
When an uncharged body is brought into contact with a charged body, charge is transferred until both bodies reach the same electric potential. The amount of charge transferred depends on the capacitance (size and shape) of the two bodies, not necessarily half of the initial charge. Therefore, this statement is incorrect.

Option (2) states: "The magnitude of charge increases with the increase in velocity of charge."
Charge is a relativistic invariant quantity. Its magnitude does not change with the velocity of the charged particle. This is a fundamental principle in physics. Therefore, this statement is incorrect.

Option (3) states: "Charge cannot exist without matter although matter can exist without charge."
Charge is an intrinsic property of elementary particles (which constitute matter). It cannot exist independently in a vacuum without being associated with a particle. So, "Charge cannot exist without matter" is correct.
Matter can exist without net charge (e.g., a neutral atom or object). So, "matter can exist without charge" (meaning without net charge) is also correct. However, matter is composed of charged particles (protons and electrons), so it always contains constituent charges. Given the potential ambiguity, let's evaluate option (4).

Option (4) states: "Repulsion is the true test of electrification (electrification means body has net charge)."
Attraction can occur between a charged body and an uncharged body (due to electrostatic induction), or between two oppositely charged bodies. However, repulsion only occurs between two bodies that are both charged with the same type of charge. Therefore, if two bodies repel each other, it is a definitive indication that both are electrified (possess a net charge). The parenthetical definition of electrification is also correct. This statement is a fundamental and unambiguous concept in electrostatics.

Comparing (3) and (4), while (3) contains generally correct statements, the phrasing "matter can exist without charge" can be ambiguous (referring to net charge vs. constituent charges). Option (4) is a universally accepted and unambiguous statement regarding the identification of charged bodies.

The final answer is $\text{4}$.