Consider the statement: For given graphs, F, G, & H, if F = G H, then (F) =(G)+(H), where denotes chromatic number. Prove

Consider the statement: For given graphs, F, G, & H, if F = G ∪ H, then χ(F) =χ(G)+χ(H), where χ denotes chromatic number. Prove or disprove the statement.