True Output

How do truth tables work?

I really don't understand how you go about them (especially with ones that state something "is not the case") When constructing truth tables I dont understand how a "^" or a "v" becomes false. For example: ((Q ∧(¬¬P ∨ R))∨ ¬ { P ∧ Q}) (Peter Smith - An Introduction to Formal Logic)

Public Comments

1. You mean those STUPID T+T=T, T+F=T, etc. tables? Those are nonsence. I had to do them in college. Hated them.
2. a truth table works by demonstrated truth behind a valid argument. for example if (a), then (b), (a), therefore (b). the table will show why this is true. it looks like a matrix when you write it all out.
3. To say that something, call it A, "is not the case" is simply to says that "not A" or -A is true. Here's a little rundown on the reasoning behind truth tables: First, the meanings of the symbols are defined via truth tables, based on the ways we actually reason. This yields the "standard" or "basic" truth tables. With negation, if statement A is T, then -A is F, and vice versa. With &, both A and B must be true for the whole state A&B to be true, otherwise the statement A&B is false. With "A or B", or AvB, the statement is false only when both A and B are false, otherwise the statement is true. The conditional statement, "if A, then B", or A-->B is false only when A is T and B is F; otherwise it is true. These are the basic defintions of the symbols using truth tables. When analyzing a statement, one determines it's value or validity by building up from these definitions to produce the overall value of the entire statement.