I am currently trying to learn how to simplify logical expressions. But I got stuck on this one task were I am to prove that the expression is either a tautology or a contradiction. I would like some help with simplifying the following expression:
(a and not b) or (not a or b)
I am not sure where to start with the simplification. If anyone could tell me which law I should start with I would be very grateful.
Applying the Substitution form of De Morgan's Law to the first part,
(a and not b)becomes(not (not a or b))giving(not (not a or b)) or (not a or b).Or, doing the same to the second part,
(not a or b)becomes(not (a and not b))giving
(a and not b) or (not (a and not b)).This results in a tautology in the form "not A or A" for the first and "A or not A" for the second, after the substitution of A for the common expressions of each of the above.