# 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.

**Sample Solution-1:**

**Using union() function**

Python Code:

```
setc1 = set(["green", "blue"])
setc2 = set(["blue", "yellow"])
print("Original sets:")
print(setc1)
print(setc2)
setc = setc1.union(setc2)
print("\nUnion of above sets:")
print(setc)
setn1 = set([1, 1, 2, 3, 4, 5])
setn2 = set([1, 5, 6, 7, 8, 9])
print("\nOriginal sets:")
print(setn1)
print(setn2)
print("\nUnion of above sets:")
setn = setn1.union(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}

**Pictorial Presentation:**

## Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:

**Sample Solution-2:**

**Using | operator**

Python Code:

```
setc1 = set(["green", "blue"])
setc2 = set(["blue", "yellow"])
print("Original sets:")
print(setc1)
print(setc2)
setc = setc1 | setc2
print("\nUnion of above sets:")
print(setc)
setn1 = set([1, 1, 2, 3, 4, 5])
setn2 = set([1, 5, 6, 7, 8, 9])
print("\nOriginal sets:")
print(setn1)
print(setn2)
print("\nUnion of above sets:")
setn = setn1 | 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}

## Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:

**Sample Solution-3:**

**Union of more than two sets:**

Python Code:

```
setn1 = set([1, 1, 2, 3, 4, 5])
setn2 = set([1, 5, 6, 7, 8, 9])
setn3 = set([3, 4, 5, 3, 9, 10])
setn4 = set([5, 7, 9, 10, 12, 14])
print("\nOriginal sets:")
print(setn1)
print(setn2)
print(setn3)
print(setn4)
print("\nUnion of first three sets:")
setn = setn1.union(setn2, setn3)
print(setn)
print("\nUnion of above four sets:")
setn = setn1.union(setn2, setn3, setn4)
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}

## Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:

**Python Code Editor:**

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