Final answer:
The statement is false because genetic variability can still occur through chromosomal crossover during prophase I of meiosis, even if independent assortment in anaphase I does not occur.
Step-by-step explanation:
The statement that genetic variability will not occur among offspring if independent assortment does not occur during anaphase I of meiosis is false. Independent assortment is one mechanism that contributes to genetic diversity; it occurs during meiosis I, particularly in anaphase I, where homologous chromosomes are separated into different gametes. However, another important mechanism for creating genetic variability is chrmosomal crossover, which occurs during prophase I of meiosis. This process involves the physical exchange of chromosome segments between homologous chromosomes and leads to new combinations of alleles in the resulting gametes. Therefore, even if independent assortment were not to occur, chromosomal crossover could still provide variability in the genetic make-up of the offspring.