A Little Logic

• Negative logic is very hard to follow, and your expressions should be as simple as possible.

• DeMorgan's Laws specifie a logic rule that can often help simplify complicated negative logical expressions:

  If an expression negates a complex expression, it can be simplified by applying the logical not to each term in the expression and then changing each and to an or and each or to an and.

• Is this the correct logical expression to check for a valid test scores that is from 0 to 100?

  !((score < 0) && (score > 100))

  It is difficult to tell because of the negative logic.

• Applying DeMorgan’s law can will simplify the logical expression:

  (!(score < 0) || !(score > 100))

• This is still be hard to understand, but we can simplify it more by writing it as positive rather than negative logic:

  ((score >= 0) || (score <= 100))

• Now with the following test plan, we can see that the expression is incorrect:

  Score	Expected Result	Notes	End Result	Correct?
  95	is valid, should evaluate to true	((95 >= 0) || (95 <= 100))	true
  0	is valid, should evaluate to true	((0 >= 0) || (0 <= 100))	true
  100	is valid, should evaluate to true	((100 >= 0) || (100 <= 100))	true
  101	is not valid, should evaluate to false	((101 >= 0) || (101 <= 100))	true
  -3	is not valid, should evaluate to false	((-3 >= 0) || (-3 <= 100))	true

  Quick Review: Which tests are bounds tests? Which are branch tests? Are there any error tests?

• We can fix this expression by changing the or to an and like this:

  ((score >= 0) && (score <= 100))

•  Double check it with the test plan; is it correct?

  Score	Expected Result	Notes	End Result	Correct?
  95	is valid, should evaluate to true	((95 >= 0) && (95 <= 100))	true
  0	is valid, should evaluate to true	((0 >= 0) && (0 <= 100))	true
  100	is valid, should evaluate to true	((100 >= 0) && (100 <= 100))	true
  101	is not valid, should evaluate to false	((101 >= 0) && (101 <= 100))	false
  -3	is not valid, should evaluate to false	((-3 >= 0) && (-3 <= 100))	false

• Have a look at exercise 5.23 on pages 239 and 240 of your book for more practice using De Morgan's Law and simplifying logical expressions written using negative logic.