1. Uses for Truth Tables Determine the truth conditions for any compound statementDetermine the truth conditions for any compound statement Determine whether a statement is a tautology, a contradiction or neither,Determine whether a statement is a tautology, a contradiction or neither, Determine whether two formulae are equivalent.Determine whether two formulae are equivalent.

2. Equivalence Two formulae are said to be equivalent if, but only if, those formulae are true and false under exactly the same conditions, that is, if, but only if, the truth table columns for the dominant operators are identical.Two formulae are said to be equivalent if, but only if, those formulae are true and false under exactly the same conditions, that is, if, but only if, the truth table columns for the dominant operators are identical.

3. Testing for Equivalence n To use a truth table to test two formulae for equivalence, begin by constructing truth table columns for each formula. Use one set of guide columns for both formulae. n Compare the columns for the dominant operators of the two formulae. If the truth values agree in each row, the formulae are equivalent.

4. Truth-Table Test for Equivalence T T   ~R    T  T S F T F T S ) ::   T T ( R Are the two formulas logically equivalent? T T  T T T  T   T T Do the formulas match in truth value?YES

5. Truth-Table Test for Equivalence   T T R  ~   T  T S  T  T S ) :: ~   T T ( R~ Are the two formulas logically equivalent?    T T T T  T T   T  T  T    Do the formulas match in truth value?NO

6. Truth-Table Test for Equivalence   T T R  ~   T  T S  T  T S ) :: ~   T T ( R~ Are the two formulas logically equivalent?    T T T T  T T   T  T  T T T  Do the formulas match in truth value?YES

7. Truth-Table Test for Equivalence   T T R  ~   T  T S  T  T S ) :: ~   T T ( R~ Are the two formulas logically equivalent?  T T T T    T T   T  T  T T T  Do the formulas match in truth value?NO

8. Truth-Table Test for Equivalence   T T R  ~   T  T S  T  T S ) :: ~   T T ( R~ Are the two formulas logically equivalent?  T T T T    T T   T  T  T    Do the formulas match in truth value?YES

9. Do Not Distribute a Negation Across A Conjunction or a Disjunction! not R and not S  not ( R and S) not R or not S  not ( R or S)

10. Rather... not R and not S not ( R and S) not R or not S not ( R or S) = =