## Operations and functions for defining supersets and subsets. Comparison of sets

### Contents

- 1. Operations
**>**,**>=**. Superset. Example - 2. Operations
**<**,**<=**. Subset. Example - 3. Operations of sets comparison
**==**,**!=**. Example - 4. Function issubset(). Subset determining
- 5. Function issuperset(). Superset definition
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##### 1. Operations >, >=. Superset. Example

The operations **>**, **>=** are intended to determine if a given set is a superset of another. The result of the operations is True or False.

The general form of the operation > next

set1>set2

where

*set1*– a set that is considered as a superset. If all elements of*set2*are in the*set1*and*set1*!=*set2*(the sets are not equal), then the result of the operation is*True*. Otherwise, the result of the operation is*False*;*set2*– a set that is considered as a subset.

The general form of the operation **>=** next

set1>=set2

where *set1*, *set2 *are sets that are considered respectively as a superset and subset.

The operation **>=** returns True if one of the conditions is true:

- all elements of
*set2*are included in*set1*; *set1==set2*(sets are equal).

In operations **>**, **>=** sets cannot be empty.

**Example.**

# Sets # 1. Operation >. Determining if a set is a superset x = { 1, 2, 3 } y = { 2 } f = x > y # f = True x = { 'а', 'b', 'с' } y = { 'а', 'b', 'с' } f = x > y # f = False - sets are equal x = { 1, 2, 3 } y = { 1, 4 } f = x > y # f = False # 2. Operation >= x = { 1, 2, 3 } y = { 1, 2, 3 } f = x >= y # f = True x = { 'abc', True, 5.66 } y = { True, 5.66 } f = x >= y # f = True

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##### 2. Operations <, <=. Subset. Example

The operations **<**, **<=** are intended to determine if a given set is a subset of another. The difference between the operations **<** and **<=** occurs when the compared sets are equal to each other. If the sets are equal, then the operation **<** returns False, and the operation **<=** returns True.

The general form of the operation < next

set1<set2

where

*set1*– a set that is considered as a subset. If all elements of*set1*are placed in*set2*and the sets are not equal (*set1*!=*set2*), then the result of the operation is True;*set2*– a set that is considered as a superset.

The general form of the operation <= next

set1<=set2

where *set1*, *set2* are nonempty sets that are considered as a subset and superset.

The result of the operation **<=** is True if one of the conditions is true:

- all elements of
*set1*are included in*set2*; - sets are equal (
*set1*==*set2*).

In operations **<**, **<=** sets cannot be empty.

**Пример.**

# Sets # 1. Operation < x = { 1, 2, 3 } y = { 1, 3, 5, 2, 8, 9 } f = x < y # f = True x = { 5 } y = { 2, 'b', 7.20 } f = x < y # f = False # 2. Operation <= x = { 2.8, 2.9, 3.2 } y = { 2.9, 3.2, 2.8 } f = x <= y # f = True - sets are equal x = { 'a', 'c', 'd' } y = { 'c', 'a' } f = x <= y # f = False

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##### 3. Operations of sets comparison ==, !=. Example

The operations **==**, **!=** Are used to compare sets for equality/inequality. The result of the operations is True or False.

The general form of the equality checking **==** is as follows

set1==set2

where *set1*, *set2* – sets that are compared for equality. If the sets are equal, then True is returned, otherwise False is returned.

The general form of the inequality check operation **!=** Is as follows

set1!=set2

where *set1*, *set2* – sets that are compared on inequality. If the sets are unequal, then True is returned; otherwise, False is returned.

**Example 1.** Using the operation **==** (equality of sets).

# Sets # Operation ==. Comparison of sets for equality x = { 1, 2, 3 } y = { 1, 3, 2 } f = x == y # f = True print('f = ', f) # Definition of equality of sets in an if statement x = { 'a', 'b', 'c', 'd' } y = { 'b', 'a', 'c' } if x==y: print("Sets are equals.") else: print("Sets are not equals.")

The result of the program

f = True Sets are not equals.

**Example 2. **Using the operation **!=** (inequality comparison).

# Sets # Operation != # The use in if statement x = set('hello') y = { 'h', 'e', 'l', 'o' } print('x = ', x) print('y = ', y) if x!=y: print("Sets are not equals.") else: print("Sets are equals.")

The result of the program

x = {'h', 'l', 'e', 'o'} y = {'h', 'l', 'e', 'o'} Sets are equals.

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##### 4. Function issubset(). Subset determining

The issubset() function is designed to determine if the current set is a subset of another. The general form of function declaration is as follows

set.issubset(other)

where

*set*– current subset;*other*– another set that is compared to the entry with the set.

The issubset() function returns True if one of the conditions is true:

*set*is a subset of other. In other words, all elements of*set*are in the set*other*;- the sets
*set*and*other*are equal.

In other cases, the issubset() function returns False. The issubset() function can be replaced with the **<=** operation.

**Example.**

# Sets # Function issubset() x = { 2, 3, 4 } y = { 3, 4 } f1 = x.issubset(y) # f1 = False f2 = y.issubset(x) # f2 = True

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##### 5. Function issuperset(). Superset definition

The issuperset() function determines if the current set is a superset of another. The general function declaration form is as follows

set.superset(other)

where

*set*– current set;*other*– another set which is associated with*set*. If*set*is a superset of*other*, then the function returns True. Otherwise, the function returns False.

The issuperset() function can be replaced with the **>=** operation.

**Example.**

# Sets # Function issuperset() x = { 2, 4, 6, 8 } y = { 2, 8 } f1 = x.issuperset(y) # f1 = True f2 = y.issuperset(x) # f2 = False

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### Related topics

**Basic concepts.**Creating a set. Operation in. The set operations to create a new set- Classes set, frozenset.
**Functions**for working with sets. Purpose.**Examples** - Limitations on the use of sets. The use of class frozenset. Generators of sets

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