 Often compound statements are concealed by the language, so it's important to recognize them. The conjunction A and B should be written both A and B, but it's often written other ways. A useful way to recognize conjunctions is to keep in mind the following idea. A conjunction requires all component statements. So, for example, identify the simple statements 36 is a prime number that is square. Remember, a statement is a sentence that can be true or false, and at this point we're not worried about whether the statement is true or false. We're only worried about it as a statement. Now, this statement says two things about 36. First, 36 is a prime number. And second, 36 is a square number. Now, if we rewrite this statement as 36 is both a prime number and 36 is a square number, this says the same thing as our original statement with a few more words. And so, this says the same thing, so our statement is a conjunction of the two simple statements. Or let's take a look at another one. A duck is an aquatic bird which eats fish. A duck? Alright, who hired this intern? We'll go with it. Because remember, we're only concerned about this as a statement as something that could be true or false without worrying for now whether it is true or false. So, this statement says a few things. A duck is aquatic. It also says a duck is a bird and a duck eats fish. And if we rewrite our three statements as follows, a duck is both aquatic and a bird and eats fish. We'll use the word both here, even though it's not grammatically correct, because there's no way to say in the English language all three of the following. Wait a minute. You could say all three of the following. Never mind. In any case, the important thing here is that this statement says the same thing. Our statement is a conjunction of the three simple statements. You can eat cake, but not ice cream. So, taking this apart into our simple statements, you can eat cake, you can eat ice cream, which we negate to get the statement we actually have. And once again, if we reword this as you can eat cake and you cannot eat ice cream, this says the same thing. So, again, our statement is a conjunction of the two statements, one of which is going to be negated. How about a disjunction? The disjunction should be read either A or B. Now, disjunctions tend to be a lot more obvious. As we saw, you can state a conjunction without using the words both and. It's a lot harder to state a disjunction without using or. Still, it's useful to remember a disjunction only requires one of its components. So, you can do all the assignments or pass the final exam. And again, we should analyze this and find our simple statements. You can do all the assignments. You can pass the final exam. And again, we can rewrite this as either you can do all the assignments or you can pass the final exam. And this has the same thing, so the statement is a disjunction.