Final answer:
The Nineteenth Amendment did nearly double the number of eligible voters in the U.S. by granting voting rights to women, which accounted for roughly half of the population.
Step-by-step explanation:
The statement "The Nineteenth Amendment nearly doubled the number of eligible voters in the United States" is true. The amendment, which granted full voting rights for women nationally, was a significant expansion of the electorate. Before its ratification in 1920, women were largely disenfranchised, especially at the national level.
Harry Burn's pivotal vote in the Tennessee General Assembly, influenced by a letter from his mother, secured the necessary majority for the amendment's passage, effectively enfranchising half the population – the women of America.