Final answer:
Emperor Trajan informed Pliny the Younger that a person could prove they were not Christian by performing sacrifices to the Roman gods and venerating the emperor's image, thereby showing their loyalty to Roman traditions and the state.
Step-by-step explanation:
According to Emperor Trajan, in his correspondence with Pliny the Younger (c. 112 CE), a person could prove that he or she was not a Christian by showing a willingness to worship the Roman gods and to venerate the emperor's image through sacrifice. Trajan advised Pliny that if the accused denied being Christian and proved their loyalty to Roman gods by making an offering of wine and incense to Trajan's statue, they should be pardoned even if they had been under suspicion before. This act of sacrificing to the Roman gods and the emperor was a way to publicly affirm one's adherence to the traditional Roman religious practices and loyalty to the state, which Christians refused to do, leading to their persecution.