Truth Table
As we get to ever more complicated statements we want to have some methodology to keep track of which statements are true and which are false, the truth table help us keep track of them.
The idea is: On each row, we list a possible combination of Trues and Falses for each of the propositional variables, and then mark down whether the (molecular) statement in question is True or False in that case. We do this for every possible combination of Trues and Falses. Then we can clearly see the cases in which the statement is true or false. For complicated statements, we will first fill in values for each part of the statement, as a way of breaking up our task into smaller, more manageable pieces.
Conjunction(AND) Truth Table
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
*Truth Table
| T | F | T | F | F |
| T | F | F | T | T |
| F | T | T | F | T |
| F | T | F | T | T |