Unifying Residual ${\mathbb{Z}}_2^{23}\otimes {\mathbb{Z}}_2^{12}$ Symmetries and Quark-Lepton Complementarity

The residual ${\mathbb{Z}}_2^{23}$ (${\mathbb{Z}}_2^{\mu \tau }$) and $\mathbb Z^{12}_2$($\mathbb Z^s_2$or$\overline{\mathbb Z}^s_2$) symmetries can not only apply to the lepton sector, but also explain the mainly $1$–$2$ mixing in the quark sector. With both up and down quarks subject to the same $\mathbb Z^{23}_2$symmetry,whichinterchangesthesecondandthirdgenerations,the$1$--$3$and$2$--$3$ mixing angles in CKM vanish while the Cabibbo angle is dictated by two residual ${\mathbb{Z}}_2^{12}$ symmetries. It turns out that the quark-lepton complementarity conditions are natural consequences of unifying residual ${\mathbb{Z}}_2^{23}\otimes {\mathbb{Z}}_2^{12}$ symmetries in both lepton and quark sectors.