diff --git a/lib/rspec/matchers/built_in/has.rb b/lib/rspec/matchers/built_in/has.rb
index 4973893c4..2040a3416 100644
--- a/lib/rspec/matchers/built_in/has.rb
+++ b/lib/rspec/matchers/built_in/has.rb
@@ -78,7 +78,8 @@ def predicate_matches?(value=true)
             predicate_actual = predicate_result
             if value == !!predicate_actual && value != predicate_actual
               RSpec.deprecate(
-                "`#{predicate_method_name}` returned neither `true` nor `false`, but rather `#{predicate_actual.inspect}`")
+                "`#{predicate_method_name}` returned neither `true` nor `false`, but rather `#{predicate_actual.inspect}`",
+                :replacement => "`expect(subject.#{predicate_method_name}).to #{value ? "be_truthy" : "be_falsey"}`")
             end
             value == !!predicate_actual
           end
diff --git a/spec/rspec/matchers/built_in/be_spec.rb b/spec/rspec/matchers/built_in/be_spec.rb
index 55443c751..1be745503 100644
--- a/spec/rspec/matchers/built_in/be_spec.rb
+++ b/spec/rspec/matchers/built_in/be_spec.rb
@@ -93,11 +93,22 @@
       }.to fail_with("expected `#{actual.inspect}.happy?` to be truthy, got false")
     end
 
-    it "prints a deprecation warning" do
-      expect(RSpec).
-        to receive(:deprecate).
-        with("`infinite?` returned neither `true` nor `false`, but rather `-1`")
-      expect(-Float::INFINITY).to be_infinite
+    context "when the predicate neither returns true or false" do
+      it "prints a deprecation warning when actual is truthy" do
+        expect(RSpec).
+          to receive(:deprecate).
+          with("`infinite?` returned neither `true` nor `false`, but rather `-1`",
+               :replacement => "`expect(subject.infinite?).to be_truthy`")
+        expect(-Float::INFINITY).to be_infinite
+      end
+
+      it "prints a deprecation warning when actual is truthy" do
+        expect(RSpec).
+          to receive(:deprecate).
+          with("`infinite?` returned neither `true` nor `false`, but rather `nil`",
+               :replacement => "`expect(subject.infinite?).to be_falsey`")
+        expect(1).to_not be_infinite
+      end
     end
   end
 
diff --git a/spec/rspec/matchers/built_in/has_spec.rb b/spec/rspec/matchers/built_in/has_spec.rb
index 98975818a..7ff0699e6 100644
--- a/spec/rspec/matchers/built_in/has_spec.rb
+++ b/spec/rspec/matchers/built_in/has_spec.rb
@@ -160,12 +160,24 @@ def o.has_sym?(sym); sym == :foo; end
       expect(actual).not_to have_foo
     end
 
-    it "prints a deprecation warning" do
-      expect(RSpec).
-        to receive(:deprecate).
-        with("`has_foo?` returned neither `true` nor `false`, but rather `nil`")
-      actual = double("actual", :has_foo? => nil)
-      expect(actual).not_to have_foo
+    context "when the predicate neither returns true or false" do
+      it "prints a deprecation warning when actual is falsey" do
+        expect(RSpec).
+          to receive(:deprecate).
+          with("`has_foo?` returned neither `true` nor `false`, but rather `nil`",
+               :replacement => "`expect(subject.has_foo?).to be_falsey`")
+        actual = double("actual", :has_foo? => nil)
+        expect(actual).not_to have_foo
+      end
+
+      it "prints a deprecation warning when actual is truthy" do
+        expect(RSpec).
+          to receive(:deprecate).
+          with('`has_foo?` returned neither `true` nor `false`, but rather `"bar"`',
+               :replacement => "`expect(subject.has_foo?).to be_truthy`")
+        actual = double("actual", :has_foo? => "bar")
+        expect(actual).to have_foo
+      end
     end
   end