# Python: Union of sets

## Python sets: Exercise-7 with Solution

Write a Python program to create a union of sets.

From Wikipedia,

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero (0) sets and it is by definition equal to the empty set.

The union of two sets A and B is the set of elements which are in A, in B, or in both A and B. In symbols,

A ∪ B = {x : x ∈ A or x ∈ B}

For example, if A = {1, 3, 5, 7} and B = {1, 2, 4, 6, 7} then A ∪ B = {1, 2, 3, 4, 5, 6, 7}. A more elaborate example (involving two infinite sets) is:

A = {x is an even integer larger than 1}

B = {x is an odd integer larger than 1}

A ∪ B = {2,3,4,5,6,...}

As another example, the number 9 is not contained in the union of the set of prime numbers {2, 3, 5, 7, 11, ...} and the set of even numbers {2, 4, 6, 8, 10, ...}, because 9 is neither prime nor even.

Sets cannot have duplicate elements, so the union of the sets {1, 2, 3} and {2, 3, 4} is {1, 2, 3, 4}. Multiple occurrences of identical elements have no effect on the cardinality of a set or its contents.

**Visual Presentation:**

**Sample Solution-1:**

**Using union() function**

Python Code:

```
# Create a set 'setc1' with elements "green" and "blue":
setc1 = set(["green", "blue"])
# Create a set 'setc2' with elements "blue" and "yellow":
setc2 = set(["blue", "yellow"])
# Print a message to indicate the original sets:
print("Original sets:")
# Print the contents of 'setc1':
print(setc1)
# Print the contents of 'setc2':
print(setc2)
# Use the 'union' method to combine 'setc1' and 'setc2' into 'setc':
setc = setc1.union(setc2)
# Print a message to indicate the union of the above sets:
print("\nUnion of above sets:")
# Print the resulting 'setc', which contains all unique elements from both 'setc1' and 'setc2':
print(setc)
# Create a set 'setn1' with repeated elements, including 1, 2, 3, 4, and 5:
setn1 = set([1, 1, 2, 3, 4, 5])
# Create a set 'setn2' with elements including 1, 5, 6, 7, 8, and 9:
setn2 = set([1, 5, 6, 7, 8, 9])
# Print a message to indicate the original sets:
print("\nOriginal sets:")
# Print the contents of 'setn1' and 'setn2':
print(setn1)
print(setn2)
# Print a message to indicate the union of the above sets:
print("\nUnion of above sets:")
# Use the 'union' method to combine 'setn1' and 'setn2' into 'setn':
setn = setn1.union(setn2)
# Print the resulting 'setn', which contains all unique elements from both 'setn1' and 'setn2':
print(setn)
```

Sample Output:

Original sets: {'blue', 'green'} {'blue', 'yellow'} Union of above sets: {'blue', 'yellow', 'green'} Original sets: {1, 2, 3, 4, 5} {1, 5, 6, 7, 8, 9} Union of above sets: {1, 2, 3, 4, 5, 6, 7, 8, 9}

**Sample Solution-2:**

**Using | operator**

Python Code:

```
# Create a set 'setc1' with elements "green" and "blue":
setc1 = set(["green", "blue"])
# Create a set 'setc2' with elements "blue" and "yellow":
setc2 = set(["blue", "yellow"])
# Print a message to indicate the original sets:
print("Original sets:")
# Print the contents of 'setc1':
print(setc1)
# Print the contents of 'setc2':
print(setc2)
# Use the union operator '|' to combine 'setc1' and 'setc2' into 'setc':
setc = setc1 | setc2
# Print a message to indicate the union of the above sets:
print("\nUnion of above sets:")
# Print the resulting 'setc', which contains all unique elements from both 'setc1' and 'setc2':
print(setc)
# Create a set 'setn1' with repeated elements, including 1, 2, 3, 4, and 5:
setn1 = set([1, 1, 2, 3, 4, 5])
# Create a set 'setn2' with elements including 1, 5, 6, 7, 8, and 9:
setn2 = set([1, 5, 6, 7, 8, 9])
# Print a message to indicate the original sets:
print("\nOriginal sets:")
# Print the contents of 'setn1' and 'setn2':
print(setn1)
print(setn2)
# Print a message to indicate the union of the above sets:
print("\nUnion of above sets:")
# Use the union operator '|' to combine 'setn1' and 'setn2' into 'setn':
setn = setn1 | setn2
# Print the resulting 'setn', which contains all unique elements from both 'setn1' and 'setn2':
print(setn)
```

Sample Output:

Original sets: {'green', 'blue'} {'blue', 'yellow'} Union of above sets: {'green', 'yellow', 'blue'} Original sets: {1, 2, 3, 4, 5} {1, 5, 6, 7, 8, 9} Union of above sets: {1, 2, 3, 4, 5, 6, 7, 8, 9}

**Sample Solution-3:**

**Union of more than two sets:**

Python Code:

```
# Create a set 'setn1' with repeated elements, including 1, 2, 3, 4, and 5:
setn1 = set([1, 1, 2, 3, 4, 5])
# Create a set 'setn2' with elements including 1, 5, 6, 7, 8, and 9:
setn2 = set([1, 5, 6, 7, 8, 9])
# Create a set 'setn3' with repeated elements, including 3, 4, 5, 9, and 10:
setn3 = set([3, 4, 5, 3, 9, 10])
# Create a set 'setn4' with elements including 5, 7, 9, 10, 12, and 14:
setn4 = set([5, 7, 9, 10, 12, 14])
# Print a message to indicate the original sets:
print("\nOriginal sets:")
# Print the contents of 'setn1', 'setn2', 'setn3', and 'setn4':
print(setn1)
print(setn2)
print(setn3)
print(setn4)
# Print a message to indicate the union of the first three sets:
print("\nUnion of first three sets:")
# Use the 'union' method to combine 'setn1', 'setn2', and 'setn3' into 'setn':
setn = setn1.union(setn2, setn3)
# Print the resulting 'setn', which contains all unique elements from the first three sets:
print(setn)
# Print a message to indicate the union of the above four sets:
print("\nUnion of above four sets:")
# Use the 'union' method to combine 'setn1', 'setn2', 'setn3', and 'setn4' into 'setn':
setn = setn1.union(setn2, setn3, setn4)
# Print the resulting 'setn', which contains all unique elements from all four sets:
print(setn)
```

Sample Output:

Original sets: {1, 2, 3, 4, 5} {1, 5, 6, 7, 8, 9} {3, 4, 5, 9, 10} {5, 7, 9, 10, 12, 14} Union of first three sets: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Union of above four sets: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14}

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