Common Mistakes When Using Truth Tables in Logical Reasoning

1. Not Making a Complete Table:

   • One big mistake is not listing all the rows needed for every possible truth situation.
   • For example, if we are using two variables, we should have $2^2 = 4$ rows in our truth table.
   • Some people accidentally make only 3 rows or forget some combinations.

2. Getting Logical Operators Wrong:

   • Confusing logical operators like AND, OR, and NOT can lead to mistakes.
   • For example, the truth table for $p \land q$ (which means "p AND q") should only be true if both $p$ and $q$ are true.
   • Sadly, about 30% of students make mistakes with this.

3. Not Seeing When Two Statements Mean the Same Thing:

   • Many students don't notice when two statements are actually logically the same.
   • This can cause them to create different truth tables.
   • Research shows that almost 40% of beginners get confused by more complicated expressions.

4. Forgetting About Parentheses in Complex Statements:

   • If parentheses are misplaced or left out completely, it can create wrong results.
   • Take a statement like $(p \land q) \lor r$ (which means "p AND q OR r").
   • If we don’t follow the order of operations carefully, we might end up with the wrong answer.

5. Not Double-Checking Results:

   • Lastly, some students forget to check their final results.
   • This can lead to about 20% of mistakes in logical reasoning.
   • Regularly comparing their results with known truth values can help avoid these errors.