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# Sage Project
# Ashley Garvey
# 1) How do you formulate a set in sage?
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x = set({1, 2, 5 ,6})
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x
︡6d7601ba-f3bc-40cf-8755-7ed824320db6︡{"stdout":"{1, 2, 5, 6}\n"}︡{"done":true}
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y = set({0, 3, 7, 8})
︡da369554-8e86-4029-98b2-194f3e693f5d︡{"done":true}
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y
︡258d7945-2901-4015-bbf8-1edc4c75ad74︡{"stdout":"{0, 8, 3, 7}\n"}︡{"done":true}
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# The first step is to name the set.
# Then you must use the equal sign (=).
# Lastly you must write set{()} and the elements of the set go within the parenthesis
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# 2) How do you find the intersection of two sets?
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x & y
︡fa44c29f-8128-4f8f-a501-fa7ece71e61f︡{"stdout":"set()\n"}︡{"done":true}
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# The intersection of two sets are all the elements that are included in both sets
# To fint the intersection on sage we use the & sign
# If we calculate the intersection of x & y we get the empty set since no elements of the set x are in the set y.
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# 3) How do you find the union of two sets?
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x | y
︡84fa6999-7c2f-42f9-9cdb-d87c1f5632be︡{"stdout":"{0, 1, 2, 3, 5, 6, 7, 8}\n"}︡{"done":true}
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# The union of two sets are the elements from both sets combined into a larger set
# To find the union of a set we use the | symbol.
# The union of the sets x | y is {0, 1, 2, 3, 5, 6, 7, 8}
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# 4) How do you find the complete set of subsets of a set?
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subsets(x)
︡b52eeba1-1966-4088-803a-ec134b5827f2︡{"stdout":"<generator object powerset at 0x7fcb5fc469e0>\n"}︡{"done":true}
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list(subsets(x))
︡05ed7cb5-b326-40a6-80a1-5fa0d1ea3927︡{"stdout":"[[], [1], [2], [1, 2], [5], [1, 5], [2, 5], [1, 2, 5], [6], [1, 6], [2, 6], [1, 2, 6], [5, 6], [1, 5, 6], [2, 5, 6], [1, 2, 5, 6]]\n"}︡{"done":true}
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subsets(y)
︡caf7284c-2694-448c-8352-2fbb17fc697f︡{"stdout":"<generator object powerset at 0x7ff462bce430>\n"}︡{"done":true}
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list(subsets(y))
︡331027a3-f135-41ae-9715-f5650c4f03e3︡{"stdout":"[[], [0], [8], [0, 8], [3], [0, 3], [8, 3], [0, 8, 3], [7], [0, 7], [8, 7], [0, 8, 7], [3, 7], [0, 3, 7], [8, 3, 7], [0, 8, 3, 7]]\n"}︡{"done":true}
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# To find the complete list of subsets of two sets you first have the generate the sets. To do this you have to do subsets(x).
# Then you have to list the set. to do this you have to type list(subsets(x)).
# This will list out all the subsets of the set x.
