Set in Python (2)

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*Memo:

• My post explains a set (1).
• My post explains a set (3).
• My post explains a set (4).

A non-empty set and empty set are:

• True and False, checking them with bool() respectively.
• False and True, inverting their truth values with not keyword respectively.

# Non-empty set
print(bool({0}))
print(bool({frozenset()}))
# True

# Empty set
print(bool(set()))
# False

# Non-empty set
print(not {0})
print(not {frozenset()})
# False

# Empty set
print(not set())
# True

A set can be checked if a specific element is and isn't in the set with in keyword and with not and in keyword respectively as shown below:

A = {10, frozenset([20, 30])}

print(10 in A)
print({20, 30} in A)
# True

print(20 in A)
print(30 in A)
print({10} in v)
print({20} in v)
print({30} in v)
print({10, frozenset([20, 30])} in A)
print(set() in A)
# False

A = {10, frozenset([20, 30])}

print(10 not in A)
print({20, 30} not in A)
# False

print(20 not in A)
print(30 not in A)
print({10} not in A)
print({20} not in A)
print({30} not in A)
print({10, frozenset([20, 30])} not in A)
print(set() not in A)
# True

A set can be checked if the set is and isn't referred to by two variables with is keyword and with is and not keyword respectively as shown below:

*Memo:

• Set literals with is keyword and with is and not keyword don't get warnings respectively.

A = {10, 20, 30}
B = {10, 20, 30}
C = A

print(A is B) # False
print(A is C) # True

print(A is not B) # True
print(A is not C) # False

print({10, 20, 30} is {10, 20, 30}) # False
print({10, 20, 30} is {10, 20})     # False

print({10, 20, 30} is not {10, 20, 30}) # True
print({10, 20, 30} is not {10, 20})     # True

A set and other set can be checked if all the elements in:

• them are and aren't the same with == and != respectively.
• the set are in other set with <=.
• other set are in the set with >=.
• the set and other elements are in other set with <.
• other set and other elements are in the set with >.

A = {10, 20, 30}

print(A == {10, 20, 30})     # True
print(A == {10, 20, 40})     # False
print(A == {10, 20})         # False
print(A == {10, 40})         # False
print(A == {10, 20, 30, 40}) # False
print(A == {10, 20, 40, 50}) # False
print(A == set())            # False

A = {10, 20, 30}

print(A != {10, 20, 30})     # False
print(A != {10, 20, 40})     # True
print(A != {10, 20})         # True
print(A != {10, 40})         # True
print(A != {10, 20, 30, 40}) # True
print(A != {10, 20, 40, 50}) # True
print(A != set())            # True

A = {10, 20, 30}

print(A <= {10, 20, 30})     # True
print(A <= {10, 20, 40})     # False
print(A <= {10, 20})         # False
print(A <= {10, 40})         # False
print(A <= {10, 20, 30, 40}) # True
print(A <= {10, 20, 40, 50}) # False
print(A <= set())            # False

A = {10, 20, 30}

print(A >= {10, 20, 30})     # True
print(A >= {10, 20, 40})     # False
print(A >= {10, 20})         # True
print(A >= {10, 40})         # False
print(A >= {10, 20, 30, 40}) # False
print(A >= {10, 20, 40, 50}) # False
print(A >= set())            # True

A = {10, 20, 30}

print(A < {10, 20, 30})     # False
print(A < {10, 20, 40})     # False
print(A < {10, 20})         # False
print(A < {10, 40})         # False
print(A < {10, 20, 30, 40}) # True
print(A < {10, 20, 40, 50}) # False
print(A < set())            # False

A = {10, 20, 30}

print(A > {10, 20, 30})     # False
print(A > {10, 20, 40})     # False
print(A > {10, 20})         # True
print(A > {10, 40})         # False
print(A > {10, 20, 30, 40}) # False
print(A > {10, 20, 40, 50}) # False
print(A > set())            # True

A set and other set can be checked if they have and don't have their common elements with bool() and & and with not keyword and & respectively as shown below:

A = {10, 20, 30}

print(bool(A & {20, 40})) # True
print(bool(A & {40, 50})) # False
print(bool(A & set()))    # False

print(not (A & {20, 40})) # False
print(not (A & {40, 50})) # True
print(not (A & set()))    # True

A set cannot be enlarged with * and a number as shown below:

A = {10, 20, 30, 40, 50} * 3
# TypeError: unsupported operand type(s) for *: 'set' and 'int'

A set and other sets cannot be concatenated with + as shown below:

A = {10, 20, 30} + {30, 40} + {50, 60, 70, 80}
# TypeError: unsupported operand type(s) for +: 'set' and 'set'

A set and other set can return:

• all the elements in them with '|' (Union: A ∪ B).
• their common elements with '&' (Intersection: A ∩ B).
• the elements in the set which aren't in other set with '-' (Difference: A - B).
• the elements in either the set or other set but not both with '^' (Symmetric Difference: A Δ B).

A = {10, 50}
B = {10, 30, 50}
C = {10, 20, 40, 50}

print(A | B)
# {50, 10, 30}

print(A | C)
# {50, 20, 40, 10}

print(B | C)
# {50, 20, 40, 10, 30}

print(A | B | C)
# {50, 20, 40, 10, 30}

A = {10, 20, 30, 40}
B = {10, 30, 50}
C = {30, 40}

print(A & B)
# {10, 30}

print(A & C)
# {40, 30}

print(B & C)
# {30}

print(A & B & C)
# {30}

A = {10, 20, 30, 40}
B = {10, 30, 50}
C = {30, 40}

print(A - B)
# {40, 20}

print(A - C)
# {10, 20}

print(B & C)
# {30}

print(A - B - C)
# {20}

A = {10, 20, 30, 40}
B = {10, 30, 50}
C = {30, 40}

print(A ^ B)
# {40, 50, 20}

print(A ^ C)
# {10, 20}

print(B ^ C)
# {40, 10, 50}

print(A ^ B ^ C)
# {50, 20, 30}