What??? I didn't catch what you don't like the definition of? What are you using this for? Logic for computer programming or Logic in general? Basically, those things you listed (AND, OR, XOR, =, NOT) are basic operations in Logic and computer logic. You'd probably need to find many-valued logic to find any other possible operations. I don't know.
Oh, wait, by ---> you mean implication. Like: A --> B (A implies B) And its truth table, (T=True, F=False): [table="width: 300"] [tr] [td]A[/td] [td]-->[/td] [td]B[/td] [td]Result:[/td] [/tr] [tr] [td]T[/td] [td] [/td] [td]T[/td] [td]T[/td] [/tr] [tr] [td]T[/td] [td] [/td] [td]F[/td] [td]F[/td] [/tr] [tr] [td]F[/td] [td] [/td] [td]T[/td] [td]T[/td] [/tr] [tr] [td]F[/td] [td] [/td] [td]F[/td] [td]T[/td] [/tr] [/table] Example: If you read the book (A), then you're a good Logistician (B). This statement is true unless you've read the book and you're still not a good logistician.
Look up Karnaugh maps, they will provide you the solution to any truth table, with any number of variables, using simpler logic. Even XOR can be "reduced" to (A x !B) + (!A x B). Here x stands for multiplication or AND, and ! stands for NOT, and + stands for addition or OR. The solution to your problem is !A + B, i.e. (NOT A) OR B.
Thanks for all answers. I do not like the definition of --->, it is dumb. B ---> A, if B is false, then B--> A is true, this is dumb. can we define a new symbol, |----->, that is, if I am in NY, then I am in USA. also, if X > 100, then X>2.
You're conflating natural language logic with formal logic. Yes, it makes no sense ("dumb") in natural language terms, but it's just a logical/mathematical definition that doesn't require conformance to everyday language. It's like the square root of -1. It makes no natural sense, but it's damn useful for solving a multitude of real world problems. The same goes for infinity. Infinity doesn't make sense, nothing goes on forever, but many times having dimensions go to infinity makes solving a particular problem trivial.
It's perfectly fine to use the existing --> symbol in your examples. I am in NY --> I am in USA X > 100 --> X > 2 That means exactly the same thing as the sentences you wrote down. The first part means if B is true then A is true. That's all. It doesn't tell us anything about A if B is false. Let's use your example: I am in NY --> I am in USA If I am in NY, I am in the USA. If I am not in NY, I could be in the USA or in any another country. If I am in the USA, I could be in NY or somewhere else in the USA. If I am not in the USA, I am not in NY.
no, I do not like the "--->" definition. since "if I am in Mars, then I am the president of USA" is true. it is dumb. I know in most cases, it is like a promise, example, "if I have $10,000,000, I will give you $10." in my definition of "|--->", There are sets and their subsets. it is more reasonable. Examples, if I am in NY, then I am in USA. if I am not in USA, then I am not in NY.
