How do you create a truth table for multiple operators?

To create a truth table for multiple operators, you list all possible combinations of inputs and determine the output for each.

A truth table is a mathematical table used in logic to compute the functional values of logical expressions on each of their functional arguments. It is used to illustrate the possible outcomes of a set of logical operations. When dealing with multiple operators, the process of creating a truth table becomes a bit more complex, but it's still manageable.

Firstly, you need to identify all the variables in your logical expression. For example, if you have an expression like (p AND q) OR r, your variables are p, q, and r.

Next, you need to list all possible combinations of truth values for these variables. If you have three variables, there will be 2^3 or 8 combinations. Write these combinations in rows in your table.

Now, you need to determine the truth value of the expression for each combination of inputs. Start by evaluating the innermost parentheses first. In our example, you would first determine the truth value of (p AND q) for each row. Write these values in a new column in your table.

Then, you evaluate the next part of the expression using the values you just calculated. In our example, you would now determine the truth value of (p AND q) OR r for each row. Write these values in another new column in your table.

Remember that the AND operator returns true if both inputs are true, the OR operator returns true if at least one of the inputs is true, and the NOT operator returns the opposite of the input.

By following these steps, you can create a truth table for any logical expression, no matter how many operators it contains. This is a powerful tool for understanding and analysing the behaviour of logical expressions in computer science.