This formulation for a 2 component reaction is equivalent to the selection rules for a [p + q]-cycloaddition reactions shown in the following table:
If the total number of electrons is 4n + 2, then one is in the bottom row of the table.  The reaction is thermally allowed if it is suprafacial with respect to both components or antarafacial with respect to both components.  That is to say the number of antarafacial components is even (it is 0 or 2).  Similarly if the total number of electrons is 4n, then one is in the top row of the table.  This is thermally allowed if it is suprafacial with respect to one component and antarafacial with respect to the other.  Thus the total number of antarafacial components is always odd as it is always 1.
The following are some common ground state (i.e. thermal) reaction classes analyzed in light of the generalized Woodward–Hoffmann rules.