Biconditional - SQL

The biconditional p ↔ q can be expressed in Tutorial D by p = q and the same is true of SQL. The question then arises as to whether, in SQL, p = q is equivalent to (¬p ∨ q) ∧ (¬q ∨ p). This matter is investigated in the truth table of Figure.

Figure: SQL p = q ≡ (¬p ∨ q) ∧ (¬q ∨ p)

As you can see, the equivalence does hold in SQL, but only because SQL treats unknown as not equal to-i.e., not the same truth value as-itself ! This treatment of p = q is consistent with the general rule that applies when NULL is an operand of a comparison in SQL.

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