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Update and rename boolean_algrebra.json to boolean-algrebra.json 

* Added spaces between operators
* Fixed aliases
* Renamed the file to boolean-algebra.json
master
Gautam krishna.R 2015-08-25 09:37:01 +05:30
parent 26a4b505ba
commit d4e6417842
1 changed files with 33 additions and 34 deletions
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67
share/goodie/cheat_sheets/json/boolean_algrebra.json → share/goodie/cheat_sheets/json/boolean-algrebra.json
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@ -8,8 +8,7 @@
"sourceUrl": "https://en.wikipedia.org/wiki/Boolean_algebra"
},
"aliases": [
"boolean algebra",
"logic",
"boolean logic",
"mathematical logic"
],
"section_order": [
@ -45,149 +44,149 @@
"Basic Principles": [
{
"key": "X+0=X"
"key": "X + 0 = X"
},
{
"key": "X+1=1"
"key": "X + 1 = 1"
},
{
"key": "X•1=X"
"key": "X • 1 = X"
},
{
"key": "X•0=0"
"key": "X • 0 = 0"
}
],
"Idempotent Law": [
{
"key": "X+X=X"
"key": "X + X = X"
},
{
"key": "X•X=X"
"key": "X • X = X"
}
],
"Involution law": [
{
"key": "(X)'=X"
"key": "(X)' = X"
}
],
"Law of complementarity": [
{
"key": "X+X'=1"
"key": "X + X' = 1"
},
{
"key": "X•X'=0"
"key": "X • X' = 0"
}
],
"Commutative law": [
{
"key": "X+Y=Y+X"
"key": "X + Y = Y + X"
},
{
"key": "X•Y=Y•X"
"key": "X • Y = Y • X"
}
],
"Assosiative law": [
{
"key": "(X+Y)+Z=X+(Y+Z)=X+Y+Z"
"key": "(X + Y) + Z = X + (Y + Z) = X + Y + Z"
},
{
"key": "(XY)Z=X(YZ)=XYZ"
"key": "(XY)Z = X(YZ) = XYZ"
}
],
"Distributive law": [
{
"key": "X(Y+Z)=XY+XZ"
"key": "X(Y + Z) = XY + XZ"
},
{
"key": "X+YZ=(X+Y)(X+Z)"
"key": "X + YZ = (X + Y)(X + Z)"
}
],
"DeMorgan’s law": [
{
"key": "(X+Y+Z+…)'=X'Y'Z'…"
"key": "(X + Y + Z +…)' = X'Y'Z'…"
},
{
"key": "(XYZ…)'=X'+Y'+Z'+…"
"key": "(XYZ…)' = X' + Y' + Z' +…"
},
{
"key": "[f( X,X,…X,0,1,+,•)]'=f( X',X', … X', 1, 0, •,+)"
"key": "[f( X,X,…X,0,1,+,•)]' = f( X',X', … X', 1, 0, •,+)"
}
],
"Duality": [
{
"key": "(X+Y+Z+…)D=XYZ…"
"key": "(X + Y + Z +…)D = XYZ…"
},
{
"key": "(XYZ…)D=X+Y+Z+…"
"key": "(XYZ…)D = X + Y + Z +…"
},
{
"key": "[f(X1,X2,…XN,0,1,+,•)]D=f(X1,X2,…XN,1,0,•,+)"
"key": "[f(X1,X2,…XN,0,1,+,•)]D = f(X1,X2,…XN,1,0,•,+)"
}
],
"Theorem for multiplying out and factoring": [
{
"key": "(X+Y)(X'+Z)=XZ+X'Y"
"key": "(X + Y)(X' + Z) = XZ + X'Y"
},
{
"key": "XY+X'Z=(X+Z)(X'+Y)"
"key": "XY + X'Z = (X + Z)(X' + Y)"
}
],
"Consensus theorem": [
{
"key": "XY+YZ+X'Z=XY+X'Z"
"key": "XY + YZ + X'Z = XY + X'Z"
},
{
"key": "(X+Y)(Y+Z)(X'+Z)=(X+Y)(X'+Z)"
"key": "(X + Y)(Y + Z)(X' + Z) = (X + Y)(X' + Z)"
}
],
"Simplification Theorems": [
{
"key": "XY+XY'=X"
"key": "XY + XY'= X"
},
{
"key": "(X+Y)(X+Y')=X"
"key": "(X + Y)(X + Y') = X"
},
{
"key": "X+XY=X"
"key": "X + XY = X"
},
{
"key": "X(X+Y)=X"
"key": "X(X + Y) = X"
},
{
"key": "(X+Y')Y=XY"
"key": "(X + Y')Y = XY"
},
{
"key": "XY'+Y=X+Y"
"key": "XY'+ Y = X + Y"
}
]
}
}
}