diff --git a/core/src/main/scala/cats/UnorderedFoldable.scala b/core/src/main/scala/cats/UnorderedFoldable.scala
index a6a88d215a..4336908d1f 100644
--- a/core/src/main/scala/cats/UnorderedFoldable.scala
+++ b/core/src/main/scala/cats/UnorderedFoldable.scala
@@ -29,7 +29,7 @@ import cats.instances.long._
    * If there are no elements, the result is `false`.
    */
   def exists[A](fa: F[A])(p: A => Boolean): Boolean =
-    unorderedFoldMap(fa)(a => Eval.later(p(a)))(UnorderedFoldable.commutativeMonoidEval(UnorderedFoldable.orMonoid)).value
+    unorderedFoldMap(fa)(a => Eval.later(p(a)))(UnorderedFoldable.orEvalMonoid).value
 
   /**
    * Check whether all elements satisfy the predicate.
@@ -37,7 +37,7 @@ import cats.instances.long._
    * If there are no elements, the result is `true`.
    */
   def forall[A](fa: F[A])(p: A => Boolean): Boolean =
-    unorderedFoldMap(fa)(a => Eval.later(p(a)))(UnorderedFoldable.commutativeMonoidEval(UnorderedFoldable.andMonoid)).value
+    unorderedFoldMap(fa)(a => Eval.later(p(a)))(UnorderedFoldable.andEvalMonoid).value
 
   /**
    * The size of this UnorderedFoldable.
@@ -51,19 +51,23 @@ import cats.instances.long._
 }
 
 object UnorderedFoldable {
-  private val orMonoid: CommutativeMonoid[Boolean] = new CommutativeMonoid[Boolean] {
-    val empty: Boolean = false
+  private val orEvalMonoid: CommutativeMonoid[Eval[Boolean]] = new CommutativeMonoid[Eval[Boolean]] {
+    val empty: Eval[Boolean] = Eval.False
 
-    def combine(x: Boolean, y: Boolean): Boolean = x || y
+    def combine(lx: Eval[Boolean], ly: Eval[Boolean]): Eval[Boolean] =
+      lx.flatMap {
+        case true  => Eval.True
+        case false => ly
+      }
   }
 
-  private val andMonoid: CommutativeMonoid[Boolean] = new CommutativeMonoid[Boolean] {
-    val empty: Boolean = true
+  private val andEvalMonoid: CommutativeMonoid[Eval[Boolean]] = new CommutativeMonoid[Eval[Boolean]] {
+    val empty: Eval[Boolean] = Eval.True
 
-    def combine(x: Boolean, y: Boolean): Boolean = x && y
+    def combine(lx: Eval[Boolean], ly: Eval[Boolean]): Eval[Boolean] =
+      lx.flatMap {
+        case true  => ly
+        case false => Eval.False
+      }
   }
-
-  private def commutativeMonoidEval[A: CommutativeMonoid]: CommutativeMonoid[Eval[A]] =
-    new EvalMonoid[A] with CommutativeMonoid[Eval[A]] { val algebra = Monoid[A] }
-
 }
diff --git a/core/src/main/scala/cats/data/NonEmptyChain.scala b/core/src/main/scala/cats/data/NonEmptyChain.scala
index c1ae0faf8b..035ae7e097 100644
--- a/core/src/main/scala/cats/data/NonEmptyChain.scala
+++ b/core/src/main/scala/cats/data/NonEmptyChain.scala
@@ -452,7 +452,7 @@ sealed abstract private[data] class NonEmptyChainInstances extends NonEmptyChain
         fa.foldLeft(b)(f)
 
       override def foldRight[A, B](fa: NonEmptyChain[A], lb: Eval[B])(f: (A, Eval[B]) => Eval[B]): Eval[B] =
-        fa.foldRight(lb)(f)
+        Foldable[Chain].foldRight(fa.toChain, lb)(f)
 
       override def foldMap[A, B](fa: NonEmptyChain[A])(f: A => B)(implicit B: Monoid[B]): B =
         B.combineAll(fa.toChain.iterator.map(f))
diff --git a/core/src/main/scala/cats/instances/map.scala b/core/src/main/scala/cats/instances/map.scala
index e5669de7c6..ff7dc0c264 100644
--- a/core/src/main/scala/cats/instances/map.scala
+++ b/core/src/main/scala/cats/instances/map.scala
@@ -84,6 +84,10 @@ trait MapInstances extends cats.kernel.instances.MapInstances {
       override def unorderedFold[A](fa: Map[K, A])(implicit A: CommutativeMonoid[A]): A =
         A.combineAll(fa.values)
 
+      override def forall[A](fa: Map[K, A])(p: A => Boolean): Boolean = fa.forall(pair => p(pair._2))
+
+      override def exists[A](fa: Map[K, A])(p: A => Boolean): Boolean = fa.exists(pair => p(pair._2))
+
     }
   // scalastyle:on method.length
 
diff --git a/core/src/main/scala/cats/instances/set.scala b/core/src/main/scala/cats/instances/set.scala
index ba62b96b63..6abb316fce 100644
--- a/core/src/main/scala/cats/instances/set.scala
+++ b/core/src/main/scala/cats/instances/set.scala
@@ -32,7 +32,11 @@ trait SetInstances extends cats.kernel.instances.SetInstances {
       override def forall[A](fa: Set[A])(p: A => Boolean): Boolean =
         fa.forall(p)
 
+      override def exists[A](fa: Set[A])(p: A => Boolean): Boolean =
+        fa.exists(p)
+
       override def isEmpty[A](fa: Set[A]): Boolean = fa.isEmpty
+
     }
 
   implicit def catsStdShowForSet[A: Show]: Show[Set[A]] = new Show[Set[A]] {
diff --git a/laws/src/main/scala/cats/laws/FoldableLaws.scala b/laws/src/main/scala/cats/laws/FoldableLaws.scala
index 64cb6e83ca..b959ec4be0 100644
--- a/laws/src/main/scala/cats/laws/FoldableLaws.scala
+++ b/laws/src/main/scala/cats/laws/FoldableLaws.scala
@@ -8,6 +8,16 @@ import scala.collection.mutable
 trait FoldableLaws[F[_]] extends UnorderedFoldableLaws[F] {
   implicit def F: Foldable[F]
 
+  def foldRightLazy[A](fa: F[A]): Boolean = {
+    var i = 0
+    F.foldRight(fa, Eval.now("empty")) { (_, _) =>
+        i += 1
+        Eval.now("not empty")
+      }
+      .value
+    i == (if (F.isEmpty(fa)) 0 else 1)
+  }
+
   def leftFoldConsistentWithFoldMap[A, B](
     fa: F[A],
     f: A => B
diff --git a/laws/src/main/scala/cats/laws/UnorderedFoldableLaws.scala b/laws/src/main/scala/cats/laws/UnorderedFoldableLaws.scala
index 7df29a0c3e..45b765c7ee 100644
--- a/laws/src/main/scala/cats/laws/UnorderedFoldableLaws.scala
+++ b/laws/src/main/scala/cats/laws/UnorderedFoldableLaws.scala
@@ -24,7 +24,7 @@ trait UnorderedFoldableLaws[F[_]] {
   def existsLazy[A](fa: F[A]): Boolean = {
     var i = 0
     F.exists(fa) { _ =>
-      i = i + 1
+      i += 1
       true
     }
     i == (if (F.isEmpty(fa)) 0 else 1)
@@ -33,7 +33,7 @@ trait UnorderedFoldableLaws[F[_]] {
   def forallLazy[A](fa: F[A]): Boolean = {
     var i = 0
     F.forall(fa) { _ =>
-      i = i + 1
+      i += 1
       false
     }
     i == (if (F.isEmpty(fa)) 0 else 1)
diff --git a/laws/src/main/scala/cats/laws/discipline/FoldableTests.scala b/laws/src/main/scala/cats/laws/discipline/FoldableTests.scala
index 65d10b2081..2ef720cef2 100644
--- a/laws/src/main/scala/cats/laws/discipline/FoldableTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/FoldableTests.scala
@@ -27,10 +27,9 @@ trait FoldableTests[F[_]] extends UnorderedFoldableTests[F] {
       parent = Some(unorderedFoldable[A, B]),
       "foldLeft consistent with foldMap" -> forAll(laws.leftFoldConsistentWithFoldMap[A, B] _),
       "foldRight consistent with foldMap" -> forAll(laws.rightFoldConsistentWithFoldMap[A, B] _),
+      "foldRight is lazy" -> forAll(laws.foldRightLazy[A] _),
       "ordered constistency" -> forAll(laws.orderedConsistency[A] _),
       "exists consistent with find" -> forAll(laws.existsConsistentWithFind[A] _),
-      "exists is lazy" -> forAll(laws.existsLazy[A] _),
-      "forall is lazy" -> forAll(laws.forallLazy[A] _),
       "foldM identity" -> forAll(laws.foldMIdentity[A, B] _),
       "reduceLeftOption consistent with reduceLeftToOption" ->
         forAll(laws.reduceLeftOptionConsistentWithReduceLeftToOption[A] _),
diff --git a/laws/src/main/scala/cats/laws/discipline/UnorderedFoldableTests.scala b/laws/src/main/scala/cats/laws/discipline/UnorderedFoldableTests.scala
index 321e84a5f0..2ec35220de 100644
--- a/laws/src/main/scala/cats/laws/discipline/UnorderedFoldableTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/UnorderedFoldableTests.scala
@@ -25,7 +25,9 @@ trait UnorderedFoldableTests[F[_]] extends Laws {
       "unorderedFold consistent with unorderedFoldMap" -> forAll(laws.unorderedFoldConsistentWithUnorderedFoldMap[A] _),
       "forall consistent with exists" -> forAll(laws.forallConsistentWithExists[A] _),
       "forall true if empty" -> forAll(laws.forallEmpty[A] _),
-      "nonEmpty reference" -> forAll(laws.nonEmptyRef[A] _)
+      "nonEmpty reference" -> forAll(laws.nonEmptyRef[A] _),
+      "exists is lazy" -> forAll(laws.existsLazy[A] _),
+      "forall is lazy" -> forAll(laws.forallLazy[A] _)
     )
 }
 
diff --git a/tests/src/test/scala/cats/tests/UnorderedFoldableSuite.scala b/tests/src/test/scala/cats/tests/UnorderedFoldableSuite.scala
index 3970fdc441..e6e85b6282 100644
--- a/tests/src/test/scala/cats/tests/UnorderedFoldableSuite.scala
+++ b/tests/src/test/scala/cats/tests/UnorderedFoldableSuite.scala
@@ -4,8 +4,10 @@ package tests
 import org.scalacheck.Arbitrary
 import cats.instances.all._
 import cats.kernel.CommutativeMonoid
+import cats.laws.discipline.UnorderedFoldableTests
 
-sealed abstract class UnorderedFoldableSuite[F[_]](name: String)(implicit ArbFString: Arbitrary[F[String]])
+sealed abstract class UnorderedFoldableSuite[F[_]](name: String)(implicit ArbFString: Arbitrary[F[String]],
+                                                                 ArbFInt: Arbitrary[F[Int]])
     extends CatsSuite {
 
   def iterator[T](fa: F[T]): Iterator[T]
@@ -42,6 +44,7 @@ sealed abstract class UnorderedFoldableSuite[F[_]](name: String)(implicit ArbFSt
       fa.count(Function.const(true)) should ===(fa.size)
     }
   }
+  checkAll("F[Int]", UnorderedFoldableTests[F](instance).unorderedFoldable[Int, Int])
 }
 
 final class UnorderedFoldableSetSuite extends UnorderedFoldableSuite[Set]("set") {