Hypernym for "conjunction" and "disjunction"

What you are looking for is probably logical connective, also called logical operator. Disjunction and conjunction are examples of binary logical operators.

From Wikipedia:

In logic, a logical connective (also called a logical operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the sense of the compound sentence produced depends only on the original sentences.

P.S. Conventionally and etymologically, the correct term is hyperonym, not hypernym, since the Greek word for "name" is onoma/onuma, beginning with an o; hence syn-onym and an-onym-ous, not synnym and anymous.