The fallacy of logos is "the last time it rained, our local sports team won. It is raining today, so they will win tonight". It's logos because in order to persuade a target audience it uses a statement empowered by logic. The logical reasoning suggests that if the last time the match was played was raining and they won, now that it's raining again, the will win again. The logical thought is that when it rains, the local team wins.
The fallacy of pathos is "If we don't pass this environmental protection bill now, the world will probably end soon". It's pathos because this fallacy tries to persuade by provoking certain emotions or feelings to readers. In this way, the statement is more appalling to the reader and it feels more emotionally attached to it. By talking about the end of the world, the writer is trying to evoke feelings of awareness, sorrow and frightening. So by provoking these feelings, readers may become more aware and concerned about the environmental changes that the human kind needs to make now in order to prevent the complete destruction of our world.
The fallacy of ethos is "My favorite teacher said that we should vote for Mr.Martinez, so I believe he is the best". It's ethos because the writer is convincing people by the credibility or authority of the speaker. In this case, the teacher represents a credible and respectful figure. So the reader decides to vote for whom the teacher said just because THE teacher said that.