2021-05-01-205601.sagews

# Sage Project
# Ashley Garvey
# Set Operations

# 1) How do you formulate a set in sage?

x = set({1, 2, 5 ,6})

x

{1, 2, 5, 6}

y = set({0, 3, 7, 8})

y

{0, 8, 3, 7}

# 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

# 2) How do you find the intersection of two sets?

x & y

set()

# The intersection of two sets is 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.

# 3) How do you find the union of two sets?

x | y

{0, 1, 2, 3, 5, 6, 7, 8}

# 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}

# 4) How do you find the complete set of subsets of a set?

subsets(x)

<generator object powerset at 0x7fc03be6a9e0>

list(subsets(x))

[[], [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]]

subsets(y)

<generator object powerset at 0x7fc03be6a9e0>

list(subsets(y))

[[], [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]]

# 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.

# 5) How do you check the identity of a set? how about multiple sets

3 in x

False

8 in x

False

1 in x

True

1 in x, 3 in y

(True, True)

0 in x, 4 in y

(False, False)

# You can cehck the identity of each set by asking sage if an element is in the set. For example 0 in x, sage will return false.
# This is the case for asking mulitple sets as well but we would jsut place a comma between the sets.

# from class

# Find all the elements of x that are not in y. [LKG]

x.difference(y)

{1, 2, 5, 6}