Disjunction (OR, ∨)

Again we have nine rows instead of just four and again, when unknown is not involved, the rows are as for 2VL. Also, when anything is paired with true, the result is true, as in 2VL. Our intuition, that "p or q" is true exactly when at least one operand is true, is preserved.

Figure: The SQL Truth Table for Disjunction

Now, in the theory book it is noted that disjunction could equally well be defined in terms of conjunction and negation, as

p ∨ q ≡ ¬ (¬ p ∧ ¬ q)

and the truth table in Figure is given as proof of that equivalence. The question arises, does the same equivalence hold in SQL? To answer that we need to look at the revised Figure.

Figure: SQL Disjunction in Terms of SQL Negation and SQL Conjunction