# 05 - Double Negation

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

1

FALSE

P AND P

TRUE

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

NOT NOT A (double negative) = "A"

NOT A + A = "A"

NOT A = "A"

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

3. The following correctly depicts double negation. FALSE

TRUE

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)`

single negation

de Morgan's

double negation

commutative

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

cancel each other out.

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

duplicate each other to produce a double NOT

produce an output that is always a '1'

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

b

1

NOT b

0

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

converts it into a zero (false)

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

converts it into a 1 (true)

flips it back again

8. NOT(NOT(d AND f)) =

d AND f

NOT d and f

NOT d + f

NOT d

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

It is not raining

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

It maybe raining

it is raining

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.

FALSE

TRUE