diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala
index d2b5c4f18802..afb2358b8fb1 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala
@@ -462,6 +462,11 @@ object BooleanSimplification extends Rule[LogicalPlan] with PredicateHelper {
         case (_, Literal(false, BooleanType)) => Literal(false)
         // a && a  =>  a
         case (l, r) if l fastEquals r => l
+        // a && (not(a) || b) => a && b
+        case (l, Or(l1, r)) if (Not(l) == l1) => And(l, r)
+        case (l, Or(r, l1)) if (Not(l) == l1) => And(l, r)
+        case (Or(l, l1), r) if (l1 == Not(r)) => And(l, r)
+        case (Or(l1, l), r) if (l1 == Not(r)) => And(l, r)
         // (a || b) && (a || c)  =>  a || (b && c)
         case _ =>
           // 1. Split left and right to get the disjunctive predicates,
@@ -540,6 +545,10 @@ object BooleanSimplification extends Rule[LogicalPlan] with PredicateHelper {
         case LessThan(l, r) => GreaterThanOrEqual(l, r)
         // not(l <= r)  =>  l > r
         case LessThanOrEqual(l, r) => GreaterThan(l, r)
+        // not(l || r) => not(l) && not(r)
+        case Or(l, r) => And(Not(l), Not(r))
+        // not(l && r) => not(l) or not(r)
+        case And(l, r) => Or(Not(l), Not(r))
         // not(not(e))  =>  e
         case Not(e) => e
         case _ => not
diff --git a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/BooleanSimplificationSuite.scala b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/BooleanSimplificationSuite.scala
index 1877cff1334b..1389ec98e758 100644
--- a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/BooleanSimplificationSuite.scala
+++ b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/BooleanSimplificationSuite.scala
@@ -89,6 +89,26 @@ class BooleanSimplificationSuite extends PlanTest with PredicateHelper {
       ('a === 'b || 'b > 3 && 'a > 3 && 'a < 5))
   }
 
+  test("a && (!a || b)") {
+    checkCondition('a && (!'a || 'b ), 'a && 'b)
+
+    checkCondition('a && ('b || !'a ), 'a && 'b)
+
+    checkCondition((!'a || 'b ) && 'a, 'b && 'a)
+
+    checkCondition(('b || !'a ) && 'a, 'b && 'a)
+  }
+
+  test("DeMorgan's law") {
+    checkCondition(!('a && 'b), !'a || !'b)
+
+    checkCondition(!('a || 'b), !'a && !'b)
+
+    checkCondition(!(('a && 'b) || ('c && 'd)), (!'a || !'b) && (!'c || !'d))
+
+    checkCondition(!(('a || 'b) && ('c || 'd)), (!'a && !'b) || (!'c && !'d))
+  }
+
   private val caseInsensitiveAnalyzer =
     new Analyzer(EmptyCatalog, EmptyFunctionRegistry, new SimpleCatalystConf(false))