Calculating the truth-value of a compound statement:

 

Order of work:

1. Put truth-values under all capital letters

2. Apply tildes that are to the immediate left of capital letters

3. Apply tildes that are to the immediate left of tildes that are to the immediate left of capital letters (repeat as necessary)

4. Calculate truth-values for connecting operators inside the smallest sets of parentheses (those that contain no other parentheses)

5. Calculate truth-values for tildes that have only the smallest sets of parentheses in their scope

6. Repeat steps 4 and 5 for larger and larger parenthetical groupings until only the main operator has no truth-value beneath it; calculate its truth-value and youíre doneóthatís the truth-value of the entire compound statement.