Question

Write a proof sequence for the following assertion. Justify one of the steps in your proof using the result of Example 1.8.
not(a and notb)
notb

implies nota

Answer 1

I think you will need one of De Morgan's Laws to do this.

De Morgan's laws
(Philosophy / Logic) (in formal logic and set theory) the principles that conjunction and disjunction, or union and intersection, are dual.
**Thus the negation of P & Q is equivalent to not-P or not-Q**
[named after Augustus De Morgan (1806-71), British mathematician]

http://tinyurl.com/cvpt2mm

Answer 2

For your posted first expression: not(a and notb)

Write it symbolically as ~(a ^ ~b) --> The character ^ means "and."
Then, given: notb which is ~b in symbolic form.
Show: nota which is ~a in symbolic form.

Answer 3

The task is to show that ~(a ^ ~b) implies ~a if given ~b.
------------------------------------

~(a ^ ~b) ==> ~a V ~(~b) ==> ~a V b.

~a V b
~b
_______
Therefore, ? @malia667

Answer 4

Yes that sounds right. thanks!