There's already an empty-set sequence in
/usr/share/X11/locale/en_US.UTF-8/Compose:
<Multi_key> <braceleft> <braceright> : "∅" U2205 # EMPTY SET
I'll just use that one.
<Multi_key> <A> <A> : "∀" U2200 # FOR ALL
<Multi_key> <d> <d> : "∂" U2202 # PARTIAL DIFFERENTIAL
<Multi_key> <E> <E> : "∃" U2202 # THERE EXISTS
-<Multi_key> <0> <0> : "∅" U2205 # EMPTY SET
<Multi_key> <D> <D> : "∆" U2206 # INCREMENT (Laplace operator)
<Multi_key> <N> <N> : "∇" U2207 # NABLA (gradient)