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05 - Double Negation

 1. In ordinary 'negation', if P = TRUE, then NOT P will always be ___________

  P AND P

  FALSE

  1

  TRUE

 2. Double negation is best described by which of the following statements?

  NOT A + A = "A"

  NOT NOT NOT A (double NOT negative) = "A"

  NOT A = "A"

  NOT NOT A (double negative) = "A"

 3. The following correctly depicts double negation.
doublenegation1.png

  TRUE

  FALSE

 4. The following is an example/depiction of ___________laws.
NOT(a AND b) = NOT(a) OR NOT(b), NOT (a OR b) = NOT(a) AND NOT(b)

  de Morgan's

  double negation

  commutative

  single negation

 5. The double negation law states that if you negate a negation (ie if you have a NOT within a NOT) they effectively ___________________

  produce an output that is always a '1'

  produce an output of a '0', given any given inputs

  duplicate each other to produce a double NOT

  cancel each other out.

 6. According to double negation: NOT(NOT(b)) =

  1

  0

  b

  NOT b

 7. In the following equation: NOT(NOT(a)) = a, the first NOT flips the value of b, then the second NOT ______________________________

  flips it back again

  converts it into a zero (false)

  converts it into a 1 (true)

  flips it twice more so that the output is always the same as the input x b

 8. NOT(NOT(d AND f)) =

  d AND f

  NOT d and f

  NOT d

  NOT d + f

 9. Applying the laws of 'double negation' the statement: "it is false that it is not raining." is the same as saying:

  it is raining

  It is not raining

  It maybe raining

  It is not raining and it is raining (i.e a paradox has arisen)

 10. An example statement that includes the double negation principle would be: if a statement is true, then it is not the case that it is false.

  TRUE

  FALSE