One classic example of a syllogism is "All men are mortal. Socrates is a man. Socrates is mortal." A syllogism is a logical argument that forms a set of three conclusions with the first two conclusions justifying the third.
Because syllogism relies on three different components to prove a supposed truth, the third conclusion can be true or false. For example, a syllogism can prove something that is true: "All dogs are mammals. A beagle is a dog. A beagle is a mammal." But a syllogism can also show faulty logic. For example: "Sharks kill people. A whale shark is a shark. Whale sharks kill people." This is, of course, not true. Whale sharks are peaceful toward humans; they don't even have teeth. But, this shows the logical thought process that can go into justifying a false belief.