diff --git a/pkgs/racket-pkgs/racket-doc/scribblings/reference/sets.scrbl b/pkgs/racket-pkgs/racket-doc/scribblings/reference/sets.scrbl
index 8c76e1ed5c..438f713624 100644
--- a/pkgs/racket-pkgs/racket-doc/scribblings/reference/sets.scrbl
+++ b/pkgs/racket-pkgs/racket-doc/scribblings/reference/sets.scrbl
@@ -78,7 +78,7 @@ returns @racket[#f] otherwise.
 }
 
 @deftogether[(
-@defproc[(set-immutable? [x any/c]) boolean?]
+@defproc[(set? [x any/c]) boolean?]
 @defproc[(set-mutable? [x any/c]) boolean?]
 @defproc[(set-weak? [x any/c]) boolean?]
 )]{
@@ -90,9 +90,9 @@ returns @racket[#f] otherwise.
 }
 
 @deftogether[(
-@defproc[(set [v any/c] ...) (and/c generic-set? set-equal? set-immutable?)]
-@defproc[(seteqv [v any/c] ...) (and/c generic-set? set-eqv? set-immutable?)]
-@defproc[(seteq [v any/c] ...) (and/c generic-set? set-eq? set-immutable?)]
+@defproc[(set [v any/c] ...) (and/c generic-set? set-equal? set?)]
+@defproc[(seteqv [v any/c] ...) (and/c generic-set? set-eqv? set?)]
+@defproc[(seteq [v any/c] ...) (and/c generic-set? set-eq? set?)]
 @defproc[(mutable-set [v any/c] ...) (and/c generic-set? set-equal? set-mutable?)]
 @defproc[(mutable-seteqv [v any/c] ...) (and/c generic-set? set-eqv? set-mutable?)]
 @defproc[(mutable-seteq [v any/c] ...) (and/c generic-set? set-eq? set-mutable?)]
@@ -110,9 +110,9 @@ replaced by a later element that is @racket[equal?] or @racket[eqv?] but not
 }
 
 @deftogether[(
-@defproc[(list->set [lst list?]) (and/c generic-set? set-equal? set-immutable?)]
-@defproc[(list->seteqv [lst list?]) (and/c generic-set? set-eqv? set-immutable?)]
-@defproc[(list->seteq [lst list?]) (and/c generic-set? set-eq? set-immutable?)]
+@defproc[(list->set [lst list?]) (and/c generic-set? set-equal? set?)]
+@defproc[(list->seteqv [lst list?]) (and/c generic-set? set-eqv? set?)]
+@defproc[(list->seteq [lst list?]) (and/c generic-set? set-eq? set?)]
 @defproc[(list->mutable-set [lst list?]) (and/c generic-set? set-equal? set-mutable?)]
 @defproc[(list->mutable-seteqv [lst list?]) (and/c generic-set? set-eqv? set-mutable?)]
 @defproc[(list->mutable-seteq [lst list?]) (and/c generic-set? set-eq? set-mutable?)]
diff --git a/racket/collects/racket/private/set-types.rkt b/racket/collects/racket/private/set-types.rkt
index 47140fff14..2b76fb6f69 100644
--- a/racket/collects/racket/private/set-types.rkt
+++ b/racket/collects/racket/private/set-types.rkt
@@ -14,7 +14,7 @@
          list->weak-set list->weak-seteq list->weak-seteqv
          list->mutable-set list->mutable-seteq list->mutable-seteqv
          set-eq? set-eqv? set-equal?
-         set-weak? set-mutable? set-immutable?
+         set-weak? set-mutable? set?
          for/set for/seteq for/seteqv
          for*/set for*/seteq for*/seteqv
          for/weak-set for/weak-seteq for/weak-seteqv
@@ -776,8 +776,8 @@
   (dprintf "set-equal?\n")
   (and (custom-set? x) (hash-equal? (custom-set-table x))))
 
-(define (set-immutable? x)
-  (dprintf "set-immutable?\n")
+(define (set? x)
+  (dprintf "set?\n")
   (immutable-custom-set? x))
 (define (set-mutable? x)
   (dprintf "set-mutable?\n")
diff --git a/racket/collects/racket/set.rkt b/racket/collects/racket/set.rkt
index d5e0786587..7f385a1198 100644
--- a/racket/collects/racket/set.rkt
+++ b/racket/collects/racket/set.rkt
@@ -28,7 +28,7 @@
       [(mutable-or-weak) (or/c set-weak? set-mutable?)]
       [(mutable) set-mutable?]
       [(weak) set-weak?]
-      [(immutable) set-immutable?]
+      [(immutable) set?]
       [else (raise-arguments-error 'set/c
                                    "invalid #:kind argument"
                                    "#:kind argument" kind)]))
@@ -81,7 +81,7 @@
       [(mutable-or-weak) (lambda (x) (or (set-mutable? x) (set-weak? x)))]
       [(mutable) set-mutable?]
       [(weak) set-weak?]
-      [(immutable) set-immutable?]))
+      [(immutable) set?]))
   (lambda (x)
     (and (generic-set? x) (cmp? x) (kind? x))))
 
@@ -109,7 +109,7 @@
      (unless (set-weak? x)
        (raise-blame-error b x "expected a weak set"))]
     [(immutable)
-     (unless (set-immutable? x)
+     (unless (set? x)
        (raise-blame-error b x "expected an immutable set"))]))
 
 (define (set-contract-projection mode)