The burning of a piece of magnesium wire is a synthesis reaction.
Synthesis reaction: It is the type of reaction in which two different atom reacts to form different molecule or compound.
Burning of a piece of magnesium(Mg) wire in the air(oxygen) results in the production of Magnesium oxide(MgO).
2Mg(s) + O2(g)2MgO(s)
Hence is a synthesis reaction.
Final statement: True, The burning of a piece of magnesium wire is a synthesis reaction.