AND (both classes)
var list = document.getElementsByClassName("class1 class2");
var list = document.querySelectorAll(".class1.class2");
OR (at least one class)
var list = document.querySelectorAll(".class1,.class2");
XOR (one class but not the other)
var list = document.querySelectorAll(".class1:not(.class2),.class2:not(.class1)");
NAND (not both classes)
var list = document.querySelectorAll(":not(.class1),:not(.class2)");
NOR (not any of the two classes)
var list = document.querySelectorAll(":not(.class1):not(.class2)");