Final answer:
Genes in eukaryotes are not only composed of exons but also contain introns that are removed during mRNA processing.
Step-by-step explanation:
Eukaryotic genes are composed of exons, which correspond to protein-coding sequences, and intervening sequences called introns. Introns are removed from the pre-mRNA during processing. Intron sequences in mRNA do not encode functional proteins. Therefore, the statement that genes in eukaryotes are only composed of exons that are themselves composed of codons is false.