Why was the inca empire defeated? choose all answers that are correct.
a. the inca learned from the aztecs’ mistakes and killed every spaniard they encountered.
b. disease ravaged the inca empire.
c. pizarro sailed down the east coast of south america to argentina.
d. the spanish sent messages of peace and friendship to the inca.
e. pizarro took atahualpa hostage and then had him executed.

"e. Pizarro took Atahualpa hostage and then had him executed" is the best answer from the list since these destabilized the empire greatly. 

a. The Inca learned from the Aztecs’ mistakes and killed every Spaniard they encountered.
This is historically incorrect, but even if it was correct, this would not be a logical reason to as why they were defeated, as it is inferring the Inca were stronger than the Spanish.

b. Disease ravaged the Inca Empire.
This is correct. One of the main reasons the Europeans were able to colonize the Americas was disease. The natives, like the Incas, weren't immune to European diseases, so they spread quickly and killed many.

c. Pizarro sailed down the east coast of South America to Argentina.
This has nothing to do with why they would be defeated.

d. The Spanish sent messages of peace and friendship to the Inca.
Again, this is both historically inaccurate and and illogical answer. 

e. Pizarro took Atahualpa hostage and then had him executed.
This is also correct. After Atahualpa was executed, the Incan Empire was thrown into a bit of chaos, as they had just lost their ruler, who was seen as almost godlike.