This is a conjunction in discrete mathematics. For example, if r=q∧p, then r is true (or 1) if and only if both p and q are true (or both 1).

On the contrary, to analyze (xi), take a conjunction and read it as disjunction, such as r=p∨q, r is true (or 1) if and only if at least one of p and q is true (or at least one of p and q is 1).

These are all in mathematical logic. If q is true, its value is 1, and if it is false, its value is 0.