Symbolic Logic explores the principles of formal reasoning and the use of symbols to represent logical expressions.
A truth table lists every possible combination of truth values for the given propositions. It helps us understand how logical connectives work together.
Two statements are logically equivalent if they always have the same truth value, no matter what. We use this to check if two arguments are really saying the same thing.
The statement \( \lnot(\lnot p) \) is always equivalent to \( p \), which we can see using a truth table.
| \( p \) | \( \lnot p \) | \( \lnot(\lnot p) \) |
|---|---|---|
| T | F | T |
| F | T | F |
Checking if \( p \rightarrow q \) and \( \lnot p \lor q \) are logically equivalent using a truth table.
Proving that \( p \lor \lnot p \) is always true—this is called a tautology.
Truth tables help us compare logical statements and see if they are really the same.