{
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"Chapter 1: Sets\n",
"========"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 1, Page 03:\n",
"----------------------"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Therefore, the solution set of the given equation can be written in roaster form as {-2,1}\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"#Variable declaration\n",
"coeff = [1,1,-2]\n",
"\n",
"#Calculations\n",
"roots_array = np.roots(coeff)\n",
"\n",
"#Result\n",
"print \"Therefore, the solution set of the given equation can be written in roaster form as {%d,%d}\"%(roots_array[0],roots_array[1])\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 2, Page 03:\n",
"---------------------"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The required numbers are 1,2,3,4,5,6\n",
"So, the given set in the roster form is {1,2,3,4,5,6}\n"
]
}
],
"source": [
"#Variable declaration\n",
"pos_integer = []\n",
"\n",
"#Calculations\n",
"for i in range(1,1000): #1000 is taken as the upper limit of a positive integer\n",
" if i**2<40:\n",
" pos_integer.append(i)\n",
" \n",
"#Result\n",
"print \"The required numbers are %d,%d,%d,%d,%d,%d\"%(pos_integer[0],pos_integer[1],pos_integer[2],pos_integer[3],pos_integer[4],pos_integer[5])\n",
"print \"So, the given set in the roster form is {%d,%d,%d,%d,%d,%d}\"%(pos_integer[0],pos_integer[1],pos_integer[2],pos_integer[3],pos_integer[4],pos_integer[5])\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 12, Page 14:\n",
"-----------------------"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The union of the two given arrays is \n",
"[ 2 4 6 8 10 12]\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"#Variable declaration\n",
"a = [2,4,6,8]\n",
"b = [6,8,10,12]\n",
"\n",
"#Calculations\n",
"union_array = np.union1d(a,b)\n",
"\n",
"#Result\n",
"print \"The union of the two given arrays is \"\n",
"print union_array"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 13, Page 14:\n",
"-----------------------"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A U B = ['a' 'e' 'i' 'o' 'u']\n",
"A = ['a', 'e', 'i', 'o', 'u']\n",
"Thus, A U B = A\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"#Variable declaration\n",
"a = ['a','e','i','o','u']\n",
"b = ['a','i','u']\n",
"\n",
"#Calculations\n",
"union_array = np.union1d(a,b)\n",
"\n",
"#Result\n",
"print \"A U B = %s\"%(union_array)\n",
"print \"A = %s\"%(a)\n",
"print \"Thus, A U B = A\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 15, Page 15:\n",
"----------------------"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A intersection B = [6 8]\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"#Variable declaration\n",
"a = [2,4,6,8]\n",
"b = [6,8,10,12]\n",
"\n",
"#Calculations\n",
"intersect_array = np.intersect1d(a,b)\n",
"\n",
"#Result\n",
"print \"A intersection B = %s\"%(intersect_array)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 18, Page 17:\n",
"-----------------------"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A - B = [1 3 5]\n",
"B - A = [8]\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"#Variable declaration\n",
"a = [1,2,3,4,5,6]\n",
"b = [2,4,6,8]\n",
"\n",
"#Calculations\n",
"diff_a = np.setdiff1d(a,b)\n",
"diff_b = np.setdiff1d(b,a)\n",
"\n",
"#Result\n",
"print \"A - B = %s\"%(diff_a)\n",
"print \"B - A = %s\"%(diff_b)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 20, Page 19:\n",
"-----------------------"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A' = [ 2 4 6 8 10]\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"#Variable declaration\n",
"u = [1,2,3,4,5,6,7,8,9,10]\n",
"a = [1,3,5,7,9]\n",
"\n",
"#Calculations\n",
"complement_a = np.setdiff1d(u,a)\n",
"\n",
"#Result\n",
"print \"A' = %s\"%(complement_a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 22, Page 19:\n",
"-----------------------"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A' = [1 4 5 6]\n",
"B' = [1 2 6]\n",
"A' intersection B' = [1 6]\n",
"A U B = [2 3 4 5]\n",
"(A U B)' = [1 6]\n",
"Therefore, (A U B)' = A' intersection B' \n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"#Variable declaration\n",
"u = [1,2,3,4,5,6]\n",
"a = [2,3]\n",
"b = [3,4,5]\n",
"\n",
"#Calculations\n",
"complement_a = np.setdiff1d(u,a)\n",
"complement_b = np.setdiff1d(u,b)\n",
"intersect_ab = np.intersect1d(complement_a,complement_b)\n",
"union_ab = np.union1d(a,b)\n",
"complement_union_ab = np.setdiff1d(u,union_ab)\n",
"\n",
"#Result\n",
"print \"A' = %s\"%(complement_a)\n",
"print \"B' = %s\"%(complement_b)\n",
"print \"A' intersection B' = %s\"%(intersect_ab)\n",
"print \"A U B = %s\"%(union_ab)\n",
"print \"(A U B)' = %s\"%(complement_union_ab)\n",
"print \"Therefore, (A U B)\\' = A\\' intersection B\\' \"\n"
]
}
],
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