 For a quick review of logic, we'll look at some of the operations that we have available to us. In this course, we're primarily going to be dealing with four different operations, ands, ors, knots, and exclusibles. Once in a while, you'll see nans and nors as well. And the majority of these are binary operations. They apply to two different propositions at the same time, and produce some composite of the result. So, for example, our and operation takes two propositions, and it will return true if both of those propositions are true. If either one or both of them are false, then the and operation will also return false. Your operation, on the other hand, says that if either of our two propositions are true, then the result will be true. The knot is a unary operation, and it just inverts whatever your input is. So, truths become falses, falses become truths. The exclusive or is a little confusing to people at first. It's like an or operation, but it more closely matches what we think of as or in a natural language. In this case, our expression is only true if either a or b is true, but not if both of them are true. So, it's only true if exclusively one of the two inputs is true. The result will be false if either both inputs are true or both inputs are false. Nand and nor are really just not and and not or, so we can apply a negation to the results of our and or or operations.