In mathematical logic, the Law of Syllogism says that if the following two statements are true: (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r . Let p be the statement " you miss the bus", let q be the statement "you will be late to school", and let r be the statement "you will get detention". Then (1) and (2) can be written 1) If p , then q . 2) If q , then r . So, by the Law of Syllogism, we can deduce 3) If p , then r or If you miss the bus then you will get detention
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