Every minimal dual discriminator variety is minimal as a quasivariety

Let († ) denote the following property of a variety 𝒱 : Every subquasivariety of 𝒱 is a variety. In this paper, we prove that every idempotent dual discriminator variety has property († ) . Property († ) need not hold for nonidempotent dual discriminator varieties, but († ) does hold for minimal nonidempotent dual discriminator varieties. Combining the results for the idempotent and nonidempotent cases, we obtain that every minimal dual discriminator variety is minimal as a quasivariety