Final answer:
Rutherford B. Hayes supported public education for all black people and believed in the fostering of equality. He promoted political equality and social opportunity for all Americans.
Step-by-step explanation:
The president who supported public education for all black people and believed that it would foster equality was Rutherford B. Hayes. In his second inaugural address, he pledged to promote political equality and encouraged social opportunity for all Americans. He wanted to put the questions of reconstruction to rest and help rebuild the Republican Party around economic development.