I'm a human, I'm not a robot, and I don't have a CPU for a brain, so H is true, R is false, and C is also false. Let's try using it! First, we have to determine what the value of each identifier is. The main operator's column is highlighted this is the "output" of the statement. Each component of our statement is broken out into a column of the table. Our example is a contingency because it's possible for me to be neither a human or a robot, or I could be a robot but not have a CPU for a brain.įinally, we have a truth table for our statement. A & ~A is a contradiction because it's saying that "A is true and it's false", and it's impossible for something to be both true and false at the same time. For example, A v ~A is a tautology because if you translate it to English, it's saying that "A is true or it's false", which of course is always true regardless of what A is. Statements can also be tautologies (the statement is always true, no matter what the inputs are) or contradictions (always false).
This simply means that the statement could either be true or false, depending on whether the inputs (the identifiers) are true or false. Next, you'll see indicators showing that the statement is a contingency. There's also a "Prettify" button to replace operators like > or = with nicer-looking versions. If you added an error into the statement (like changing "&" to "&") that would go away and you'd see an error message. You should see an output like this: At the very top, there's a thumbs up emoji indicating the statement is well-formed. Now that we have a symbolic logic statement, we can generate a truth table for it. You can find a list of all logical operators here.
H v (R & C)To translate this into symbolic logic, we turned each of the atomic statements of the statement into single letter constants, and words like or and and into the corresponding logical operators ( v and &).
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