A Syllogism is a sequence of -usually two- statements and a conclusion, where the reader has to decide if the conclusion is true based on the statements, not on real world knowledge. For example: (a) Dogs are green. (b) Sophie is a dog. (c) Sophie is green.
Generally in our everyday experiences, dogs are not green, but based on the first two statements alone, the third statement is valid. The conclusion can also be inconclusive; for example: (a) Cats like milk. (b) Joe is a hamster. (c)Joe does not like milk. The first two statements have no common elements, and therefore no conclusion can validly be drawn.