diff --git a/lib/array_intersection.rb b/lib/array_intersection.rb
index ac8771f..2bad0d6 100644
--- a/lib/array_intersection.rb
+++ b/lib/array_intersection.rb
@@ -1,3 +1,38 @@
+#Time complexity: O(n+m)
+#Space complexity: O(n)
 def intersection(list1, list2)
-  raise NotImplementedError, "Intersection not implemented"
-end
\ No newline at end of file
+  
+  #create a hash with each element of the array as keys and value as true 
+  hash = {}
+  list1.each do |element|
+     hash[element] = true 
+  end
+  #find each element of list2 by the hash's keys
+  result = []
+  list2.each do |element|
+    if hash[element] == true
+      result << element
+    end
+  end
+  return result
+end
+
+# Without using the hash table 
+# def intersection(list1, list2) 
+#   result = []
+#   if list1.length >= list2.length
+#     list1.length.times do |i|
+#       if list1.include?(list2[i])
+#         result << list2[i]
+#       end
+#     end
+#     return result
+#   else
+#     list2.length.times do |i|
+#       if list2.include?(list1[i])
+#         result << list1[i]
+#       end
+#     end
+#     return result
+#   end
+# end
\ No newline at end of file
diff --git a/lib/palindrome_permutation.rb b/lib/palindrome_permutation.rb
index f113692..fdb6f22 100644
--- a/lib/palindrome_permutation.rb
+++ b/lib/palindrome_permutation.rb
@@ -1,4 +1,30 @@
+#Time complexity: O(n+m+l)
+#Space complexity: O(n^2)
 
 def palindrome_permutation?(string)
-  raise NotImplementedError, "palindrome_permutation? not implemented"
+  return true if string == ""
+
+  #Convert the string to an array of letters
+  string_array = string.chars
+
+  #reverse_string_array
+  reverse_string_array = []
+  string_array.each do |letter|
+    reverse_string_array.unshift(letter)
+  end
+
+  #create a string_hash by having each element string_array as keys
+  string_hash = {}
+ 
+  string_array.length.times do |i|
+    string_hash[string_array[i]] = reverse_string_array[i]
+  end
+  
+  #compare each key and value of the hash
+  string_hash.each do |key, value|
+    if key == value
+      return true
+    end
+  end
+  return false
 end
\ No newline at end of file
diff --git a/lib/permutations.rb b/lib/permutations.rb
index 3b08381..54429d5 100644
--- a/lib/permutations.rb
+++ b/lib/permutations.rb
@@ -1,4 +1,23 @@
-
+#Time complexity: O(n+m)
+#Space complexity: O(n)
 def permutations?(string1, string2)
-  raise NotImplementedError, "permutations? not implemented"
+  return false if (string1.length != string2.length) 
+
+  #convert both strings to arrays of letters
+  array1 = string1.chars
+  array2 = string2.chars
+
+  #create a hash by assigning each element of array1 for the keys of hash
+
+  hash = {}
+  array1.each do |letter|
+    hash[letter] = true
+  end
+
+  array2.each do |letter|
+    if hash[letter] != true
+      return false
+    end
+  end
+  return true
 end
\ No newline at end of file
diff --git a/test/palindrome_permutation_test.rb b/test/palindrome_permutation_test.rb
index e9119de..984b333 100644
--- a/test/palindrome_permutation_test.rb
+++ b/test/palindrome_permutation_test.rb
@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-xdescribe "palindrome_permutation?" do
+describe "palindrome_permutation?" do
   it "will work for hello" do
     expect(palindrome_permutation?("hello")).must_equal false
   end
diff --git a/test/permutations_test.rb b/test/permutations_test.rb
index 79da2f6..ada5ee1 100644
--- a/test/permutations_test.rb
+++ b/test/permutations_test.rb
@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-xdescribe "permutations?" do
+describe "permutations?" do
   it "returns true for empty string" do
     expect(permutations?("", "")).must_equal true
   end
@@ -13,7 +13,7 @@
     expect(permutations?("pasta", "atsap")).must_equal true
   end
 
-  it "returns true for 'pizza', 'pizza'" do
+  it "returns true for 'pizza', 'pasta'" do
     expect(permutations?("pizza", "pasta")).must_equal false
   end