I need help understanding truth tables please.
http://www.youtube.com/watch?v=98jBy8x6HHw
http://www.sparknotes.com/math/geometry3/logicstatements/section4.rhtml
thank you!
You're welcome.
Sure! I can help you understand truth tables. Truth tables are a helpful tool in logic and mathematics to determine the logical values of a given logical expression for all possible combinations of truth values of its component propositions.
To create a truth table, we start by listing all the unique combinations of truth values for the component propositions involved in the logical expression. Let's say we have two component propositions, P and Q. There are four possible combinations of truth values: (P=True, Q=True), (P=True, Q=False), (P=False, Q=True), and (P=False, Q=False).
Next, we write the logical expression using operators such as AND, OR, and NOT, and evaluate the expression for each combination of truth values. We assign the resulting truth value, either True or False, to each combination of truth values.
For example, let's say we have a logical expression "P AND Q". Here's how we can create a truth table for it:
P | Q | P AND Q
---------------
T | T | T
T | F | F
F | T | F
F | F | F
In this truth table, the column headings represent the component propositions (P and Q), and the last column represents the logical expression "P AND Q". We evaluate the expression P AND Q for each combination of truth values for P and Q to fill in the truth table.
The truth table allows us to see the output or the truth value that results from a logical expression for all possible combinations of truth values of its component propositions. It helps in understanding the behavior and properties of logical operators and in analyzing complex logical expressions.
I hope this explanation helps you understand truth tables better! If you have any further questions, feel free to ask.