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The arguments we saw in the previous movie, were of the very simplest kind. All A are B. C is an A. Therefore, C is B. In real life, you often need far more complex arguments to get to a conclusion. In most cases, these arguments require a combination of statements that relate to each other in different ways. These different ways, are signified by logical operators. The three basic operators of logic are AND, OR and NOT.
They have more formal names. AND is a conjuction. OR is a disjunction and NOT is a negation. These simple operators allow us to make complex statements about categories or groups of categories. Let's say you have a selection of cupcakes and donuts on a table. Some of them have red frosting, some have yellow frosting. You can use these operators to refer to the cupcakes and donuts, just like you would in real life. Cupcakes AND yellow, gives you a subsection of baked goods that are both cupcakes and have yellow frosting.
Donuts OR yellow gives you all the donuts plus all of the yellow cupcakes. NOT yellow gives you all the red donuts and all the red cupcakes. Conjunction AND, works mostly like it would in natural language. We use the word AND to combine two properties or events in the same way logic does. But in English and some other languages. AND is also used to imply temporal order. I went to the hairdresser and got a haircut.
Here, the AND is not the same as a logical and. It instead signifies passage of time. Disjunction OR, is even less like the word or in natural language. If I ask you, should I wear the blue shirt or the grey shirt? I'm really asking you to pick either the blue shirt or the grey shirt. Wearing both the blue and the grey shirt isn't really an option. So here, I'm not using disjunction. But instead, inferring something more. The situation stipulates that, when I say OR, what I really mean is either/or.
Disjunction works more like the famous quote from Winnie the Pooh. When rabbit said, honey or condensed milk with your bread, Pooh was so excited that he said both. In the story, Pooh is made out to sound silly by not answering the question properly, but in logic terms, his answer is correct. Or means either A or B or it can mean A and B. Pooh is actually using rabbits imprecise question to his advantage. The final operator negation or NOT is probably the easiest to understand.
If you have a statement like. The car is blue. The negation, the car is not blue simply states that the car is not belonging to the group of cars that are blue. And just like in math, you can also have a double negation. The car is not, not blue which is the same saying the car is blue. As you see, the logical operators and or and not, are not equivalent to our natural language versions. So, it's important to answer the question why this matters to us in communication. There are reason it matters is two fold.
First, if when we communicate with one another, we keep in mind that our natural language is sloppy, that we make implicit statements like the example of Rabbit and Winnie the Pooh. We can speak more logically to make our intentions clear. So instead of asking honey or condensed milk with your bread. Rabbit should ask, do you want honey or do you want condensed milk instead? This excludes the third option of both. And provides a better user experience for Pooh.
Second, as we will see later in this course, when communication is done through computers. These operators become vitally important. And knowing how they work, becomes important as computers treat them like logic operators.
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