Final answer:
The incorrect statement about the changing roles of women in society at the turn of the 20th century is (c) women over the age of 21 could vote, as women generally did not gain the right to vote until the 1920s.
Step-by-step explanation:
The question is about identifying the statement that was NOT true about the changing roles of women in society at the turn of the 20th century. Upon assessing the options, it's clear that statement (c), which asserts that women over the age of 21 could vote, is the incorrect option. Women in the United States did not gain the right to vote until the 19th Amendment was ratified in 1920, and similarly, suffrage movements around the world generally saw success in granting women the right to vote following World War I into the 1920s.
A review of the provided historical context shows that women did demand equal pay for the same job a man was doing, they were beginning to go out for the evening by themselves, and many joined social and volunteer organizations. These were indicators of the evolving role of women in society. However, the full enfranchisement for women over the age of 21, in general, did not occur until after the time frame mentioned in the question.