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