Let \(a \circ b = \frac{a + b}{2}\). Then \(\circ\) is right self-distributive.

$$a \circ (b \circ c) = (a \circ b) \circ (a \circ c)$$Let \(a \circ b = \frac{a + b}{2}\). Then \(\circ\) is left self-distributive.

$$(b \circ c) \circ a = (b \circ a) \circ (c \circ a)$$Union is self-distributive.

Disjunction is self-distributive.

Intersection is self-distributive.

Conjunction is self-distributive.