 The law of detachment uses conditional statements, if then statements, to be able to make conclusions or to be clear that you cannot make a conclusion. We're starting with the conditional statement, if a person is an engineer, then they can do geometry. Now we have Susan is an engineer, therefore we can conclude that Susan can do geometry. That is a logical conclusion. We had P, the P portion of the statement was true, therefore we can conclude that Q is also true. In the next situation, we have that Chris can do geometry. Can we conclude that Chris is an engineer? Okay, what we have in this case for Chris can do geometry is we have Q. Do we know anything about if Q then something? No we don't. We only know if P, if a person is an engineer, then they can do geometry. We don't know about if a person can do geometry. So we cannot conclude that Chris is an engineer. Another law of logic is the law of syllogism. This is a series of if P then Q, if Q then R, if R then S, and we can make conclusions about those things as long as we line them up properly. So I have if a person is an engineer, then they can do geometry. That is my first set of if P then Q. If a person can do geometry, then they know a lot about triangles. If a person knows a lot about triangles, then their favorite number is obviously 180. How can I combine these to make a new conclusion? Because I know that P is true, then I know that Q is true. And so I can say for sure that I can say that I know Q is true, therefore I know that R is true. So if a person is an engineer, then they know a lot about triangles. Because I know that R is true, I can say that S is true. So I line up my logic statements and because I know P is true, therefore Q is true, therefore R is true, therefore S is true, I can sort of skip all of that stuff, skip the middle parts and say if I know P is true, then I can say that S is true. Therefore I can make the statement that if a person is an engineer, then their favorite number is 180.