diff --git a/Assignment 1.ipynb b/Assignment 1.ipynb
index 7c69379..b0d41a5 100644
--- a/Assignment 1.ipynb	
+++ b/Assignment 1.ipynb	
@@ -19,8 +19,8 @@
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-     "end_time": "2024-01-18T21:45:24.278399500Z",
-     "start_time": "2024-01-18T21:45:24.273024200Z"
+     "end_time": "2024-01-19T18:00:01.812390600Z",
+     "start_time": "2024-01-19T18:00:01.808045100Z"
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@@ -79,8 +79,8 @@
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+     "end_time": "2024-01-19T18:00:01.833000200Z",
+     "start_time": "2024-01-19T18:00:01.813388900Z"
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@@ -124,8 +124,8 @@
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-     "end_time": "2024-01-18T21:45:24.288935300Z",
-     "start_time": "2024-01-18T21:45:24.286415200Z"
+     "end_time": "2024-01-19T18:00:01.833998900Z",
+     "start_time": "2024-01-19T18:00:01.819489500Z"
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@@ -168,8 +168,8 @@
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-     "end_time": "2024-01-18T21:45:24.296122800Z",
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+     "end_time": "2024-01-19T18:00:01.833998900Z",
+     "start_time": "2024-01-19T18:00:01.824503300Z"
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@@ -210,8 +210,8 @@
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-     "end_time": "2024-01-18T21:45:24.298113500Z",
-     "start_time": "2024-01-18T21:45:24.293966900Z"
+     "end_time": "2024-01-19T18:00:01.836315700Z",
+     "start_time": "2024-01-19T18:00:01.830000300Z"
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@@ -261,8 +261,8 @@
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-     "end_time": "2024-01-18T21:45:24.340947500Z",
-     "start_time": "2024-01-18T21:45:24.299113600Z"
+     "end_time": "2024-01-19T18:00:01.843841300Z",
+     "start_time": "2024-01-19T18:00:01.834999100Z"
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@@ -302,8 +302,8 @@
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-     "end_time": "2024-01-18T21:45:24.341947200Z",
-     "start_time": "2024-01-18T21:45:24.303632300Z"
+     "end_time": "2024-01-19T18:00:01.924237300Z",
+     "start_time": "2024-01-19T18:00:01.838835700Z"
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@@ -351,8 +351,8 @@
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-     "end_time": "2024-01-18T21:45:24.341947200Z",
-     "start_time": "2024-01-18T21:45:24.307343300Z"
+     "end_time": "2024-01-19T18:00:01.925239100Z",
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@@ -398,9 +398,9 @@
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    "source": [
-    "First it could be helpful to find the set of all valid games to compare against. This is a little tricky as first you need to know the rules of the game and encode them correctly. The rules that I have discerned are as follows:\n",
+    "First, it could be helpful to find the set of all valid games to compare against. This is a little tricky as first you need to know the rules of the game and encode them correctly as a language. The rules that I have discerned are as follows:\n",
     "1. Each valid game has 3 a's or 3 b's, denoting a victory for one side\n",
-    "2. Once it has either victories on either side, the game does not continue, and the string is complete\n",
+    "2. Once either side has won, the game does not continue, and the string is complete\n",
     "\n",
     "$$L = \\{w \\in \\{a,b\\}^* | n_a(w) = 3 \\text{ or } n_b(w) = 3 \\text{ and } w \\text{ does not end with the opposite letter}\\}$$"
    ]
@@ -412,8 +412,8 @@
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-     "end_time": "2024-01-18T21:45:24.342947100Z",
-     "start_time": "2024-01-18T21:45:24.314341500Z"
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@@ -455,7 +455,7 @@
    "source": [
     "(a) $L_1 = \\{w \\in \\{a,b\\}^* | n_a(w) = 3 \\text{ or } n_b(w) = 3 \\}$\n",
     "\n",
-    "This one is not representable with code, as the set is produces is infinite. This language places no restrictions on the length of the string, so \"aaabbbbbbbbbbbbbbbbbbbbbbbbbbb\" is a valid string in this language. So here is a few examples of valid strings in this language that are not valid in the original language L but are in this language:\n",
+    "This language is not representable with code, as the set is produces is infinite. This language places no restrictions on the length of the string, so \"aaabbbbbbbbbbbbbbbbbbbbbbbbbbb\" is a valid string in this language. So here is a few examples of valid strings in this language that are not valid in the original:\n",
     "\n",
     "1. \"aaabbbbbbbbbbbbbbbbbbbbbbbbbbb\"\n",
     "2. \"bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbaaa\"\n",
@@ -471,7 +471,7 @@
    "source": [
     "(b) $L_2 = \\{w \\in \\{a,b\\}^* | |w| \\leq 5, \\text{ and } n_a(w) = 3 \\text{ or } n_b(w) = 3 \\}$\n",
     "\n",
-    "This language has the problem is not encoding the rule that the game stops once a player has 3 a's or 3 b's. This can be seen in these strings that are valid in this language but not in the original language L:"
+    "This language differs as it is not encoding the rule that the game stops once a player has 3 a's or 3 b's. This can be seen in these strings that are valid in this language but not in the original language L:"
    ]
   },
   {
@@ -481,8 +481,8 @@
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@@ -514,7 +514,7 @@
    "source": [
     "(c) $L_3 = \\{w \\in \\{a,b\\}^* | (n_a(w) = 3 \\text{ and } n_b(w) < 3) \\text{ or } (n_b(w) = 3 \\text{ and } n_a(w) < 3) \\}$\n",
     "\n",
-    "This language has a similar problem to the previous one, in that it does not encode the rule that the game stops once a player has 3 a's or 3 b's. The difference in this language is that the limit of string length 5 is not explicitly stated, however it is encoded to be that way by saying that if there are 3 a's then there must be less than 3 b's, and vice versa. This means that the effective maximum length of the string is 5, and thus the language is equivalent to the language from the previous question.\n",
+    "This language is similar to the previous one, in that it does not encode the rule that the game stops once a player has 3 a's or 3 b's. The difference in this language is that the limit of string length 5 is not explicitly stated, however it is encoded to be that way by saying that if there are 3 a's then there must be less than 3 b's, and vice versa. This means that the effective maximum length of the string is 5, and thus the language is equivalent to the language from the previous question.\n",
     "$$\n",
     "x, y \\in \\mathbb{Z}^* \\\\\n",
     "x = 3 \\\\\n",
@@ -531,8 +531,8 @@
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