Final answer:
The statement is false. Autonomous transposons require genes for necessary enzymes like transposase to move independently. Non-autonomous transposons cannot transpose on their own without assistance from autonomous elements.
Step-by-step explanation:
The statement that autonomous elements can transpose by themselves even though they cannot produce transposase is false. Autonomous transposons, like the maize Ac element, are able to move independently because they contain all the structural and functional features necessary for transposition, including genes that code for essential enzymes like transposase. Without these enzymes, such as in the case of the maize Ds element, the non-autonomous transposons cannot transpose by themselves and require assistance from autonomous elements that can provide the necessary transposase enzyme. This contrasts with replicative transposition, where the transposon duplicates itself and the new copy moves to another location. Additionally, retrotransposons such as LINES and SINEs function differently; for instance, SINEs are non-autonomous and rely on the activity of autonomous retrotransposons for their mobility.