Final answer:
The statement about cohesins' role in compacting chromosomes to prevent tangling is false. Cohesins hold sister chromatids together while condensins help compact chromosomes.
Step-by-step explanation:
The statement that cohesins are required to make the chromosomes more compact and thus to prevent tangling between different chromosomes is false. Cohesins primarily function to hold sister chromatids together after DNA replication. During prophase I of meiosis, the homologous chromosomes are paired up and linked together by the synaptonemal complex, not by cohesins. The synaptonemal complex forms a lattice structure around the homologs, ensuring their tight pairing during metaphase I and facilitating recombination. Upon the attachment of the kinetochore to the mitotic spindle, the cohesin proteins break down, allowing the sister chromatids to separate, and the cell to eventually divide. The actual compaction and condensation of DNA into chromosomes, which helps prevent damage during cell division, is facilitated by proteins known as condensins.