diff --git a/base/broadcast.jl b/base/broadcast.jl
index 3e826c5fc7fb3..755cc3d0a8401 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -608,6 +608,7 @@ broadcastable(x::Union{AbstractArray,Number,Ref,Tuple,Broadcasted}) = x
 # Default to collecting iterables — which will error for non-iterables
 broadcastable(x) = collect(x)
 broadcastable(::Union{AbstractDict, NamedTuple}) = throw(ArgumentError("broadcasting over dictionaries and `NamedTuple`s is reserved"))
+broadcastable(::AbstractSet) = throw(ArgumentError("broadcasting over sets is not defined as their order is not defined"))
 
 ## Computation of inferred result type, for empty and concretely inferred cases only
 _broadcast_getindex_eltype(bc::Broadcasted) = Base._return_type(bc.f, eltypes(bc.args))
diff --git a/test/broadcast.jl b/test/broadcast.jl
index 8225f873952f0..aaab3b61c99a3 100644
--- a/test/broadcast.jl
+++ b/test/broadcast.jl
@@ -599,8 +599,8 @@ end
 
     @test broadcast(identity, Iterators.filter(iseven, 1:10)) == 2:2:10
     d = Dict([1,2] => 1.1, [3,2] => 0.1)
-    @test length.(keys(d)) == [2,2]
-    @test Set(exp.(Set([1,2,3]))) == Set(exp.([1,2,3]))
+    @test_broken length.(keys(d)) == [2,2] # Issue #20678
+    @test_throws ArgumentError Set(exp.(Set([1,2,3]))) == Set(exp.([1,2,3]))
 end
 
 # Test that broadcasting identity where the input and output Array shapes do not match