diff --git a/docs/release-notes/.FSharp.Core/10.0.300.md b/docs/release-notes/.FSharp.Core/10.0.300.md
index f823f462ee..3b1d0259a3 100644
--- a/docs/release-notes/.FSharp.Core/10.0.300.md
+++ b/docs/release-notes/.FSharp.Core/10.0.300.md
@@ -1,5 +1,6 @@
 ### Fixed
 
+* Optimize Set.intersect performance symmetry and preserve identity from the first set argument. ([PR #19291](https://github.com/dotnet/fsharp/pull/19291)) (Fixes #19139)
 * Fix anonymous record field ordering in LINQ expression conversion to produce consistent expression trees regardless of field declaration order. ([Issue #11131](https://github.com/dotnet/fsharp/issues/11131), [Issue #15648](https://github.com/dotnet/fsharp/issues/15648))
 * Fix array indexing in LINQ expressions to generate proper array index expressions instead of GetArray method calls, enabling LINQ providers like Azure Cosmos DB to translate array access. ([Issue #16918](https://github.com/dotnet/fsharp/issues/16918))
 * Fix tuple join conditions and groupBy operations to properly compare tuple keys using structural equality. AnonymousObject types now implement Equals and GetHashCode, enabling inline tuple joins like `join b on ((a.Id1, a.Id2) = (b.Id1, b.Id2))` to work correctly. ([Issue #7885](https://github.com/dotnet/fsharp/issues/7885), [Issue #47](https://github.com/dotnet/fsharp/issues/47))
diff --git a/src/FSharp.Core/set.fs b/src/FSharp.Core/set.fs
index df37136e38..8e2a370739 100644
--- a/src/FSharp.Core/set.fs
+++ b/src/FSharp.Core/set.fs
@@ -267,6 +267,24 @@ module internal SetTree =
                 elif c = 0 then true
                 else mem comparer k tn.Right
 
+    let rec tryGet (comparer: IComparer<'T>) k (t: SetTree<'T>) =
+        if isEmpty t then
+            ValueNone
+        else
+            let c = comparer.Compare(k, t.Key)
+
+            if t.Height = 1 then
+                if c = 0 then
+                    ValueSome t.Key
+                else
+                    ValueNone
+            else
+                let tn = asNode t
+
+                if c < 0 then tryGet comparer k tn.Left
+                elif c = 0 then ValueSome tn.Key
+                else tryGet comparer k tn.Right
+
     let rec iter f (t: SetTree<'T>) =
         if isEmpty t then
             ()
@@ -391,6 +409,24 @@ module internal SetTree =
 
                 balance comparer (union comparer t2n.Left lo) t2n.Key (union comparer t2n.Right hi)
 
+    let rec intersectionAuxFromSmall comparer a (t: SetTree<'T>) acc =
+        if isEmpty t then
+            acc
+        else if t.Height = 1 then
+            match tryGet comparer t.Key a with
+            | ValueSome v -> add comparer v acc
+            | ValueNone -> acc
+        else
+            let tn = asNode t
+            let acc = intersectionAuxFromSmall comparer a tn.Right acc
+
+            let acc =
+                match tryGet comparer tn.Key a with
+                | ValueSome v -> add comparer v acc
+                | ValueNone -> acc
+
+            intersectionAuxFromSmall comparer a tn.Left acc
+
     let rec intersectionAux comparer b (t: SetTree<'T>) acc =
         if isEmpty t then
             acc
@@ -412,7 +448,13 @@ module internal SetTree =
             intersectionAux comparer b tn.Left acc
 
     let intersection comparer a b =
-        intersectionAux comparer b a empty
+        let h1 = height a
+        let h2 = height b
+
+        if h1 <= h2 then
+            intersectionAux comparer b a empty
+        else
+            intersectionAuxFromSmall comparer a b empty
 
     let partition1 comparer f k (acc1, acc2) =
         if f k then
diff --git a/tests/FSharp.Core.UnitTests/FSharp.Core/Microsoft.FSharp.Collections/SetType.fs b/tests/FSharp.Core.UnitTests/FSharp.Core/Microsoft.FSharp.Collections/SetType.fs
index 9c1120675a..6cb7c9bc0f 100644
--- a/tests/FSharp.Core.UnitTests/FSharp.Core/Microsoft.FSharp.Collections/SetType.fs
+++ b/tests/FSharp.Core.UnitTests/FSharp.Core/Microsoft.FSharp.Collections/SetType.fs
@@ -11,6 +11,24 @@ open System.Collections.Generic
 open FSharp.Core.UnitTests.LibraryTestFx
 open Xunit
 
+
+/// This type is used to verify that Set.intersect preserves the object identity (reference) 
+/// of the first set (S1). By overriding equality to only check the 'Id' field, 
+/// we can create two objects that are "equal" but live in different memory locations.
+[<CustomEquality; CustomComparison>]
+type IntersectItem = 
+    { Id: int; Tag: string }
+    override x.Equals(obj) =
+        match obj with
+        | :? IntersectItem as other -> x.Id = other.Id
+        | _ -> false
+    override x.GetHashCode() = hash x.Id
+    interface IComparable with
+        member x.CompareTo(obj) =
+            match obj with
+            | :? IntersectItem as other -> compare x.Id other.Id
+            | _ -> invalidArg "obj" "not an IntersectItem"
+
 (*
 [Test Strategy]
 Make sure each method works on:
@@ -332,6 +350,62 @@ type SetType() =
         Assert.AreEqual(Set.maxElement fir, 6)
         Assert.AreEqual(Set.maxElement sec, 7)
 
+
+    [<Fact>]
+    member _.Intersect_PreservesIdentity() =
+        // 1. [Test Strategy] Empty set
+        let emptyA : Set<IntersectItem> = Set.empty
+        let emptyB : Set<IntersectItem> = Set.empty
+        Assert.True((Set.intersect emptyA emptyB).IsEmpty)
+        Assert.True((Set.intersect (Set.singleton {Id=1; Tag="x"}) emptyB).IsEmpty)
+
+        // 2. [Test Strategy] Single-element set & [Identity Property]
+        let item1_S1 = { Id = 1; Tag = "From_S1" }
+        let item1_S2 = { Id = 1; Tag = "From_S2" }
+        
+        let s1_single = Set.singleton item1_S1
+        let s2_single = Set.singleton item1_S2
+        
+        let resSingle = Set.intersect s1_single s2_single
+        Assert.Equal(1, resSingle.Count)
+        
+        // Identity Check: Must be EXACTLY the same object in memory as S1
+        let singleResult = Set.minElement resSingle
+        Assert.True(Object.ReferenceEquals(singleResult, item1_S1), "Single-element identity failed: Reference must come from S1")
+
+        // 3. [Test Strategy] Sets with 4 or more elements (Optimized Path Check)
+        let item5_S1 = { Id = 5; Tag = "ID5_From_S1" }
+        let item5_S2 = { Id = 5; Tag = "ID5_From_S2" }
+
+        // S1 is large: hits intersectionAuxFromSmall (The optimized path)
+        let list1 = [ for i in 1..50 -> if i = 5 then item5_S1 else { Id = i; Tag = sprintf "L%d" i } ]
+        let list2 = [ for i in 1..5 -> if i = 5 then item5_S2 else { Id = i; Tag = sprintf "R%d" i } ]
+        
+        let s1_large = Set.ofList list1
+        let s2_small = Set.ofList list2
+        
+        let resMany = Set.intersect s1_large s2_small
+        
+        // Identity Check in Loop: 
+        // We iterate through the result and ensure every common element 
+        // has the physical reference from the first set (list1)
+        resMany |> Set.iter (fun item ->
+            let originalInS1 = list1 |> List.find (fun x -> x.Id = item.Id)
+            if not (Object.ReferenceEquals(item, originalInS1)) then
+                Assert.Fail(sprintf "Identity mismatch for ID %d: Expected reference from S1 (list1), but got another instance." item.Id)
+        )
+
+        // 4. [Reversed Size Case] (Standard Path Check)
+        // S1 is small, S2 is large: hits intersectionAux (The standard path)
+        let resReversed = Set.intersect s2_small s1_large
+        
+        // Find the specific item with ID 5 in the result
+        let item5InResult = resReversed |> Set.filter (fun x -> x.Id = 5) |> Set.minElement
+        
+        // Identity Check: Since s2_small was the FIRST argument, 
+        // the result MUST contain item5_S2 (from s2_small)
+        Assert.True(Object.ReferenceEquals(item5InResult, item5_S2), "Reversed path identity failed: Reference must come from s2_small")
+
 #if NET8_0_OR_GREATER
 
 #nowarn "1204" // FS1204: This type/method is for compiler use and should not be used directly.