 The first of the above defines the conjunction \(\phi\) and \(\psi\); the second defines the disjunction \(\phi\) or \(\psi\); the third defines the biconditional \(\phi\) if and only if \(\psi\) (which we often abbreviate as iff); and the last defines the existentially quantified formula there is an \(\alpha\) such that \(\phi\). It should be noted here that instead of using a linear string of symbols to express molecular and quantified formulas, Frege developed a two-dimensional notation for such formulas. Since we won’t be using Frege’s notation for complex formulas in what follows, we need not spend time describing it  here.[1]