Need help with propositional logic!?

raystriker

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I'm really dumbstruck by this. Any help will be appreciated!
How do i go from--> (¬A ∧ ¬K) ∨ (A ∧ K)
to
(¬K ∨ A) ∧ (¬A ∨ K)?
 
Solution
Forgive my messiness.
I3cotLO.jpg

2. Apply double De Morgan so we can change the insides without messing up the logic.
3. - 4. Carry through one of the De Morgans to the insides all the way down.
5. Treat "ands" like multiplication and "ors" like +'s, foil. Discard terms that are always false (it's okay to do this, as we are or'ing terms here).
6. - 8. Carry second De Morgan negation all the way down.
Bonus logic table for part 4. :)

IncredulousP

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Forgive my messiness.
I3cotLO.jpg

2. Apply double De Morgan so we can change the insides without messing up the logic.
3. - 4. Carry through one of the De Morgans to the insides all the way down.
5. Treat "ands" like multiplication and "ors" like +'s, foil. Discard terms that are always false (it's okay to do this, as we are or'ing terms here).
6. - 8. Carry second De Morgan negation all the way down.
Bonus logic table for part 4. :)
 
Solution

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