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"> This is one of the 100 recipes of the [IPython Cookbook](http://ipython-books.github.io/), the definitive guide to high-performance scientific computing and data science in Python.\n"
]
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"source": [
"# 15.6. Finding a Boolean propositional formula from a truth table"
]
},
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"execution_count": null,
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"source": [
"from sympy import *\n",
"init_printing()"
]
},
{
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"metadata": {},
"source": [
"Let's define a few variables."
]
},
{
"cell_type": "code",
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"source": [
"var('x y z')"
]
},
{
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"source": [
"We can define propositional formulas with symbols and a few operators."
]
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{
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"execution_count": null,
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"source": [
"P = x & (y | ~z); P"
]
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"P.subs({x: True, y: False, z: True})"
]
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"source": [
"Now, we want to find a propositional formula depending on x, y, z, with the following truth table:"
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"source": [
"Let's write down all combinations that we want to evaluate to True, and those for which the outcome does not matter."
]
},
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"cell_type": "code",
"execution_count": null,
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"minterms = [[1,0,1], [1,0,0], [0,0,0]]\n",
"dontcare = [[1,1,1], [1,1,0]]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, we use the SOPform function to derive an adequate proposition."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
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"source": [
"Q = SOPform(['x', 'y', 'z'], minterms, dontcare); Q"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's test that this proposition works."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
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"outputs": [],
"source": [
"Q.subs({x: True, y: False, z: False}), Q.subs({x: False, y: True, z: True})"
]
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{
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"metadata": {},
"source": [
"> You'll find all the explanations, figures, references, and much more in the book (to be released later this summer).\n",
"\n",
"> [IPython Cookbook](http://ipython-books.github.io/), by [Cyrille Rossant](http://cyrille.rossant.net), Packt Publishing, 2014 (500 pages)."
]
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