The above examples can be used to construct logical formulae for any desired pattern of truth values given it has two components. Assume R is the desired yet unknown formula with two true and two false values and in the order. (Blogger is being stupid right now. I will have to put the truth values in row vector form... For some reason it won't let me upload another photo)
So, R = [○,○,●,●] and C1 = [○,●,●,●] C2 = [●,○,●,●] where C1 C2 are component formula. According to the above table C1 is the third column from the left and C2 is the fourth column from the left. Once the formulae are identified use a disjunction between the two component formula. C1 ∨ C2 or R ⇔ (A ∧ B) ∨ (¬A ∧ B). The formula is in what is called disjunctive normal form. It is a sequence of conjunctions divided by disjunctions.
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