#Also, any set is a subset of itself
>>> e=FiniteSet()
>>> e.is_subset(t)
True
>>> e.is_subset(s)
True
>>> s.is_subset(s)
True
>>> t.is_subset(t)
True
#A set t is a superset of another set s, if t contains all of the members contained in s.
>>> s.is_superset(t)
False
>>> t.is_superset(s)
True
#The power set of a set,s, is the set of all possible subsets of s. Any set has exactly
#2^(cardinality) subsets. i.e. The set {1,2,3} has excatcly 8 since 2^3=8
>>> s=FiniteSet(1,2,3)
>>> ps=s.powerset()
>>> ps
{EmptySet(), {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
>>> len(ps)
8
from sympy import FiniteSet
s = FiniteSet(1,2,3)
for member in s:
print(member)
from sympy import FiniteSet
s = FiniteSet(3,4,5)
t = FiniteSet(5,4,3)
s == t
s = FiniteSet(1)
t = FiniteSet(1,2)
s.is_subset(t)
t.is_subset(s)
t.is_superset(s)
s = FiniteSet(1,2,3)
ps = s.powerset()
ps
len(ps)
#is 53 prime?
for i in range(1,54):
if i == 1:
print('i = 1')
elif i == 53:
print('i = 53')
elif int(i) != 1 or int(i) != 53:
if 53%i == 0:
s = FiniteSet() # EmptySet()
# Set Repetition and Order
members = [1, 2, 3, 2]
FiniteSet(*members) # {1, 2, 3}
for member in s:
print(member) # 1, 2, 3
# Subsets -> if all the members of s are also a member of t
s = FiniteSet(1)
t = FiniteSet(1,2)
s.is_subset(t) # True
t.is_subset(s) # False
# Supersets -> if t contains all of the members contained in s
s.is_superset(t) # True
t.is_superset(s) # True
# Powerset -> is the set of all possible subsets of s
s = FiniteSet(1, 2, 3)
ps = s.powerset()
ps # {{1}, {1, 2}, {1, 3}, {1, 2, 3}, {2}, {2, 3}, {3}, EmptySet()}
len(ps) # 8
# Proper subset -> if all the members of s are also in t and t has at least one member that is not in s
s = FiniteSet(1, 2, 3)
t = FiniteSet(1, 2, 3)
s.is_proper_subset(t) # False
t.is_proper_subset(s) # False
