Final answer:
Martha Graham and Doris Humphrey wanted to create modern dance to reflect and respond to the socio-economic climate, reject old forms, and explore authentic American movement, thus statements 1), 2), and 4) are reflective of their intentions.
Step-by-step explanation:
The intentions behind Martha Graham and Doris Humphrey establishing modern dance lie within their desire to rebel against the traditional and decorative styles of dance that did not fit the post-war era's tastes. They sought to reject dance forms that borrowed from past epochs and foreign cultures (2), and in doing so, aimed to explore a dance style synonymous with American movement and identity (4).
a It should be noted, however, that they did not reject performance or symbolism for mere technical prowess (3). Rather, the new modern dancers eschewed the idea that dance should simply be a visual representation of music (5), opting instead to create a form of dance that could stand on its own as an artistic statement. Therefore, the statements that reflect the underlying intentions for what Graham and Humphrey sought in establishing modern dance are 1), 2), and 4).