In natural language “an either-or question” may be contrastive (a more useful concept than “opposite” most of the time, in semantic matters) with the My head will explode shirt (“Do you speak French or German?” – yes, I speak a bit of both). In particular, an either-or question will usually be seeking a response stating which option you choose, not mere confirmation of whether or not the situation is true (when someone asks you “Do you want tea or coffee?”, “yes” is not generally considered an appropriate response, however accurate a statement it may be, which is why logicians mostly end up having to make their own drinks).
My head will explode shirt, Hoodie, Sweater, Ladie Tee, Vneck, Bellaflowy, Kids Shirt, Unisex and Tank Top, T-shirt
Best My head will explode shirt
Wikipedia suggests a My head will explode shirt “polar” questions, seeking a yes or no answer; “alternative” questions, the type of either-or question described above, and “wh-” questions, open ended questions seeking informational answers (such as those starting with “who”, “when”, “which” and so on). It does not really make much sense to speak of “opposites” in this ternary context, though, just contrasting alternatives.