Final answer:
There is a negative correlation between total fertility rate and progressive attitudes toward family size and women's education in China, where greater educational and economic opportunities for women and advancements in gender equality have led to fewer children being born.
Step-by-step explanation:
The relationship between the total fertility rate and attitudes toward family size and women's education in China can be complex and is influenced by various socioeconomic and cultural factors.
Option (b) There is a negative correlation, which stands out as more accurate, given the evidence suggesting that with increased educational and economic opportunities for women, along with advances in gender equality and better access to contraception, women tend to have fewer children. This is a global trend observed in many countries, including China, where increased industrial activity and urban growth - leading to higher living standards and more opportunities in urban areas - have generally coincided with a decrease in family size.
In China particularly, the introduction of the one-child policy in 1979 was intended to reduce population growth. Although the policy's effectiveness is debated, it coincided with already declining fertility rates, which have continued to decrease over time. Concurrently, the Chinese government has taken steps to enhance health, education, and employment opportunities for women, which aligns with the United Nations' recommendations for lowering birth rates in a humane way.
The decline in the number of children born to a woman in China from 5.91 in 1966 to 1.6 in recent times also reflects these combined influences of policy and shifting social attitudes towards smaller family size and greater investment in women's education.