List all possible input combinations.
If the expression uses two variables, make four rows; for three variables, make eight rows. Write the values in a consistent pattern so every combination appears once.
Break the expression into smaller parts.
Identify each logical operation inside the compound expression, such as negation, conjunction, disjunction, or implication. Create a column for each part.
Fill in the table step by step.
Start with the simplest pieces, usually the individual variables. Then evaluate the inner operations before the outer ones. This keeps the work organized and reduces mistakes.
Use the meaning of each operation carefully.
Check each row against the definition of the logical connective. For example, an “and” statement is true only when both parts are true, while an “or” statement is true when at least one part is true.
Read the final column as the answer.
The last column gives the truth value of the whole compound expression for every input row. If asked to simplify the final answer, look for a pattern such as all true, all false, or the same result as a simpler part of the expression.
Review one row at a time and verify that every intermediate column was computed from the previous ones. A good final check is to compare the last column with the logic of the original expression and confirm that every row matches.
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