How to define xvalue mixed category?

Question

Are all xvalues glvalues and rvalues at the same time? Or a xvalue may be either glvalue or a rvalue?

If it's a glvalue or/xor rvalue, can you give a example for each case?

Answer 1

From cppreference:

An rvalue expression is either prvalue or xvalue.

an xvalue (an “eXpiring” value) is a glvalue that denotes an object or bit-field whose resources can be reused;

Answering your questions:

Are all xvalues glvalues and rvalues at the same time?

Yes. More specifically, rvalue is a superset of prvalue and xvalue. Thus all xvalues are rvalues, but not all rvalues are xvalues (namely, the ones that are prvalues). And by the definition above, xvalue is a reusable glvalue. So xvalues are both glvalues and rvalues.

Or a xvalue may be either glvalue or a rvalue?

No. xvalue is purely a reusable glvalue, and reusable glvalues (i.e. xvalues) are rvalues. Think move semantics.

Examples:

int a = 6;
foo(6); // 6 is a prvalue (and thus is an rvalue)
foo(a); // a is a glvalue

std::vector<int> vec = {1, 2, 3};
bar(vec);            // vec is a glvalue
bar(std::move(vec)); // std::move(vec) is an xvalue (reusable glvalue)
                     // (and thus is an rvalue)