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# Sets Formulas Class 11

Memorizing set formulas enables students to apply their knowledge in various mathematical fields like statistics, probability, geometry, and sequences. However, if the basic concept of sets formulas class 11 is not properly understood it becomes complicated for students to memorize and apply them. This article provides a list of all sets formulas along with solved examples for students to understand them better.

## List of Sets Formulas Class 11

Students can refer to the terms and list of sets formulas class 11 provided below to gain the necessary information about sets.

**Set:**Collection of objects, when defined, is called a set.**Empty set:**Empty set is a set that has no elements in it.**Finite Set:**If the number of elements can be counted, it's called a definite set.**Infinite Set:**If the number of elements cannot be counted, it's called an infinite set.**Equal Sets:**If two sets have the same elements then they are equal sets.**Subset:**If all elements of a set A are found in another set B then A is a subset of B.**Union of two sets**A ∪ B gives set having elements of both set A and set B.**Difference of two sets**A - B gives a set having only those elements of A which are not in B.- For any two sets A and B, (A ∪ B)′ = A′ ∩ B′ and ( A ∩ B )′ = A′ ∪ B′.
- If A and B are finite sets such that A ∩ B = φ, then n (A ∪ B) = n (A) + n (B). If A ∩ B ≠ φ, then n (A ∪ B) = n (A) + n (B) – n (A ∩ B).

## Applications of Sets Formulas Class 11

Sets formulas class 11 have a wide range of applications in many abstract concepts. These formulas find their use in various topics of mathematics like geometry, sequences, probability, and others. Here are some application of Sets formulas class 11:

- Sets formulas are most commonly applied in various sciences like physics, chemistry, biology as well as computer and electrical engineering. For example, In electronics, set formulas are applied to work with circuits.
- Sets formulas are also useful in business management for planning and operations.
- Sets formulas class 11 related to union, intersection and difference are applied in database management to perform queries on data tables.

## Sets Formulas Class 11 Examples

**Example 1 :** Write the set Y = {1, 8, 27, 64, 125, . . . } in set-builder form.

**Solution :** Set Y can be represented as a cube of natural numbers since each term in the set Y is a cube of natural numbers. 23 = 8, 33 = 27, 43 = 64...

So, the set builder form of Y is Y = {x : x is the cube of a natural number} or Y = {x : x = n^{3}, where n ∈ N)

**Example 2:** Let A = {x : x is a vowel} and K = { o, x, t, e}. Find A - K and K - A and verify if they are the same?

**Solution:** Set A being set of vowels would be equal to {i, o, a, e, u} ,

So, A - K = { i, a, u}

Also, K - A = { x, t} ==> Hence, we can see (K - A) is not equal to (A - K)

## Tips to Memorize Sets Formulas Class 11

- Students should get familiarized with the basics of sets formulas class 11 and their usage in problems by solving various problems related to them. Solving problems will engage students in applying the formulas several times, which will help to learn the formulas thoroughly.

- Understanding all formulas logically will help in easy memorization. It is important to go through the important concepts before moving ahead with solving problems based on sets formulas class 11.
- Taking the use of current technology, students must also try online study material like formula sheets and save them on their laptops or mobile devices for revision.

Students can download the printable **Maths Formulas Class 11** sheet from below.

## FAQs on Sets Formulas Class 11

### What are the Important Formulas Covered Under Sets Formulas Class 11?

The important formulas covered under sets formulas class 11 are:

- Union of two sets A ∪ B gives set having elements of both set A and set B.
- Difference of two sets A - B gives a set having only those elements of A which are not in B.
- For any two sets A and B, (A ∪ B)′ = A′ ∩ B′ and ( A ∩ B )′ = A′ ∪ B′.
- If A and B are finite sets such that A ∩ B = φ, then n (A ∪ B) = n (A) + n (B). If A ∩ B ≠ φ, then n (A ∪ B) = n (A) + n (B) – n (A ∩ B).

### What are the Basic Concepts Involved in Sets Formulas Class 11?

The basic concepts involved in sets formulas class 11 are empty set, finite, infinite set, subsets, disjoint set, universal set, equal set, union of sets, intersection of sets, etc. Students can also learn to apply the union and intersection formulas through the examples given in this article.

### What is it Important to Solve Various Problems Based on Sets Formulas Class 11?

Solving various problems based on Sets Formulas Class 11 will help students in getting well-versed with sets, their representations, and operations. Additionally, regular practice of these problems will help them to easily recall the formulas within seconds when required.

### How Many Formulas are There in Sets Formulas Class 11?

There are around ten important formulas and facts that the students need to know about sets formulas class 11. Hence, students are advised to go through the list of formulas given in this article to get a clear picture of the concepts and definitions regarding various terms involving sets.

### How to Memorize Sets Formulas Class 11?

The following tips will be helpful for students to remember sets formulas class 11:

- Students get a clear understanding of all concepts used in the formula and clear their doubts.
- Students must make sure to solve all the solved examples given in the textbook as it will require students to write out formulas numerous times, which will help in memorizing them better.
- Students can also save formula sheets as wallpaper on their tablets or phones to revise them.

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