1- If all of the premises are true and the argument is valid, the conclusion MUST be valid

2- If all the premises are true and the conclusion is false, the argument must be invalid.

3- If the argument is valid and the conclusion is false, at least one premise must be false.

Valid Arguments (if...then)

1- Affirming the antecedent
    If P, then Q      example: if this metal is gold, it will NOT dissolve in nitric acid. This metal is gold.
    P, therefore Q                 Therefore it will NOT dissolve in nitric acid

2- Denying the Consequence
    If P, then Q      example: If I can do long division, then I can add and subtract.
    Not Q, therefore not P  I can not add and subtract, therefore can NOT do long division

3- Chain Argument (hypothetical syllogism)
    If P, then Q      example: If money is tight, interest rates rise.
    If Q, then R                      If interest rates rise, loan volume decreases
    Therefore if P, then R   Therefore if money is tight, loan volume decreases

1- Fallacy of affirming the consequent
    If P, then Q      example: If I can do long division, then I can add and subtract.
    If Q, therefore P              If I can add and subtract, I can do long division

2- Fallacy of denying the antecedent
    If P, then Q      example: If I locked my car, it won't be stolen
    If not P, then not Q        I did not lock my car, therefore it will be stolen