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2026-01-01
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<p>138 Learners</p>
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<p>INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta</p>
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<p>Last updated on<strong>October 23, 2025</strong></p>
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<p>INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034</p>
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<p>A subset is a fundamental concept in set theory. A set is a collection of different elements, such as numbers, letters, or objects. For example, a set can be written as {a, b, c, d}. A set A is a subset of set B if every element of set A is also an element in set B. For example, if set A = {10, 20, 30, 40} and set B = {10, 20, 30, 40, 50, 60}, then set A is a subset of set B. In this article, we will learn about subsets, types of subsets, and the symbols used to represent a subset.</p>
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<p>SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)</p>
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<h2>What is a Subset?</h2>
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<p>USA - 251, Little Falls Drive, Wilmington, Delaware 19808</p>
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<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City</p>
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<p>▶</p>
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<p>VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam</p>
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<p>A subset is a<a>set</a>whose elements are also a part of another set. For instance, if all elements in the set A are a part of set B, then set A is a subset of set B. A subset is represented using the<a>symbol</a>⊆, in set theory. For example, if A = {a, b, c} and B = {a, b, c, d, e, f}, then A is a subset of B. </p>
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<p>UAE - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates</p>
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<p>To find the total<a>number</a>of subsets of a set, we use the<a>formula</a>: 2n, where n is the number of elements in the set. For example, if A = {2, 4, 6}, then the number of subsets of a set A 23 = 8. </p>
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<p>UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom</p>
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<h2>Difference Between Subset and Superset</h2>
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<p>The subset and superset are<a>types of sets</a>. If A is a subset of B, then B is a superset of A. In this section, we will discuss the difference between a subset and a superset. </p>
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Subset <p>Superset </p>
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<p>A set is said to be a subset only if all its elements are also elements of the second set</p>
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<p>A set is a superset of another set if it contains all the elements or additional elements than another set </p>
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<p>If A is a subset of B, it can be represented as A ⊆ B</p>
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<p>If set A is the superset of set B, it can be represented as A ⊇B</p>
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<p>For example, if A = {p, q, r} and B = {p, q, r, s, t}, Then A is a subset of B</p>
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<p>For example, if A = {p, q, r} and B = {p, q, r, s, t}, Then B is a superset of A</p>
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<p>The subset size is smaller than or equal to the superset.</p>
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<p>The superset has all the elements of the subset. </p>
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<h2>What are the Types of subsets?</h2>
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<p>Subsets are classified into different types based on the number of elements they have. The main types of subsets are: </p>
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<ul><li><strong>Proper Subset</strong></li>
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<li><strong>Improper Subset</strong></li>
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<li><strong>Singleton Subset</strong></li>
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</ul><p><strong>Proper Subset:</strong>A proper subset includes all sets except the set itself. For example, if A = {3, 6, 9}, then its proper subsets are {}, {3}, {6}, {9}, {3, 6}, {3, 9}, {6, 9}, but the set {3, 6, 9} is not a proper subset. If A is a proper subset of B, then it can be represented as A ⊂ B, where A ≠ B, which means elements in set A are a part of set B, but A does not have all elements of B. </p>
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<p><strong>Improper Subset:</strong>The improper subset of a set is the set itself. For example, for the set {3, 6, 9}, the improper set is {3, 6, 9}. If A ⊆ B and A = B, then A is a subset of B, but not a proper subset. </p>
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<p><strong>Singleton Subset:</strong>The subset of a set that contains only one element of the set is a singleton subset. For example, A = {5, 6, 7}, then the singleton subset will be {5}, {6}, {7}. </p>
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<h3>Explore Our Programs</h3>
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<p>No Courses Available</p>
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<h2>What is the Symbol of Subsets?</h2>
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<p>In set theory, to represent a subset, we use symbols like ⊆ and ⊂. To represent the proper subset, we use the symbol ⊂, and to represent the improper subset, we use the symbol ⊆. The symbol ⊆ is read as a subset or equal to, and ⊂ is read as a subset of. </p>
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<h2>What is a Proper Subset?</h2>
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<p>A proper subset of a set is a subset that contains some elements, but not all, elements of the original set. It does not include the set itself. For example, if A = {2, 4, 6}, then its proper subset are: {}, {2}, {4}, {6}, {2, 4}, {4, 6}, and {2, 6}, but {2, 4, 6} is a subset but not a proper subset. A proper subset can be represented using the symbol ⊂, where A ⊂ B and A ≠ B. The number of proper subsets of a set can be calculated using the formula: 2n - 1, where n is the number of elements. </p>
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<h2>What is a Subset of Real Numbers?</h2>
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<p>The numbers, including<a>positive integers</a>, negative integers,<a>fractions</a>, and<a>irrational numbers</a>, are the<a>real numbers</a>. The subset of real numbers includes:</p>
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<ul><li>Rational Numbers: The numbers in the form p/q, where p and q are integers and q ≠ 0, and include terminating and<a>repeating decimals</a>. </li>
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<li>Integers: The numbers include all the<a>whole numbers</a>and integers, including zero. </li>
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<li>Whole Numbers: The numbers include all positive numbers and zero.</li>
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<li>Natural Numbers: The numbers include all positive integers. </li>
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</ul><h2>What is a Subset of Integers?</h2>
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<h2>What is a Power Set of a Set?</h2>
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<p>The<a>power</a>set of a set includes all the possible subsets of the set, including the<a>empty set</a>and the set itself. The power set of a set is represented by p(A), where A is the original set. For example, if A = {5, 10}, then the power set of A is denoted as p(A), p(A) = {{}, {5}, {10}, {5, 10}}</p>
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<h2>Common Mistakes and How to Avoid Them in Subset</h2>
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<p>In mathematics, students often make mistakes when learning about subsets. Here are some common mistakes and the tips to avoid them in the subset. </p>
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<h2>Real-World Applications of Subset</h2>
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<p>In set theory, a subset is a fundamental concept and is used in different fields such as computer science, biology, economics, etc. In this section, we will learn a few real-world applications of subsets. </p>
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<ul><li>In online shopping platforms, subsets are used to display products based on selected criteria. For example, if you are searching for a dress in white color, under $15, then the website will show only items based on the criteria. </li>
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</ul><ul><li>In event planning and scheduling, subsets are used to represent particular<a>combinations</a>. </li>
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</ul><ul><li>In biology, to model gene regulatory networks, we use subsets.</li>
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</ul><ul><li>In economics, we use subsets to divide the market into segments based on customer characteristics. </li>
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</ul><h3>Problem 1</h3>
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<p>List all subsets of A = {1, 2}</p>
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<p>Okay, lets begin</p>
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<p>The subset of A is {}, {1}, {2}, {1, 2} </p>
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<h3>Explanation</h3>
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<p>The number of subsets of A = 2n = 22 = 4 The subset of A includes the empty set, the single set, and the set itself. So, the subsets are {}, {1}, {2}, {1, 2} </p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<p>If B = {x, y, z}, find how many subsets B has.</p>
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<p>Okay, lets begin</p>
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<p>The number of subsets of B is 8</p>
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<h3>Explanation</h3>
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<p>The number of subsets of a set = 2n Here, n = 3 So, the number of subsets of B = 23 = 8 </p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<p>Is {5, 6} ⊂ {5, 6, 7}?</p>
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<p>Okay, lets begin</p>
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<p>Yes, {5, 6} ⊂ {5, 6, 7}</p>
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<h3>Explanation</h3>
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<p> Let’s consider A = {5, 6} and B ={5, 6, 7} The elements in set A are also in set B, so set A is a proper subset of set B. So, {5, 6} ⊂ {5, 6, 7} </p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<p>List all the subsets of {4, 8, 12}?</p>
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<p>Okay, lets begin</p>
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<p>The subsets of {4, 8, 12} are {}, {4}, {8}, {12}, {4, 8}, {4, 12}, {8, 12}, {4, 8, 12}</p>
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<h3>Explanation</h3>
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<p>The subsets of a set include the empty set and all the combinations of the set. </p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<p>List all the proper and improper subsets of C = {a, b}</p>
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<p>Okay, lets begin</p>
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<p>For C, the proper subsets are {}, {a}, {b}, the improper subset is {a, b} </p>
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<h3>Explanation</h3>
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<p>A proper subset of a set has all the elements of the set, and an improper subset contains all the elements of the set.</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Subset</h2>
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<h3>1.What is a subset?</h3>
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<p>A subset is a set where all elements belong to another set; that is, if A is a subset of B, then every element of A is also an element of B. </p>
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<h3>2.What are the subsets of a = {1, 2, 3}?</h3>
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<p>The subsets of {1, 2, 3} are {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3} </p>
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<h3>3.What does a ⊂ b mean?</h3>
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<p>a ⊂ b represents that a is a proper subset of b. </p>
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<h3>4.What is the difference between ⊆ and ⊂?</h3>
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<p>⊆ is used to represent the subset, and ⊂ is used to represent the proper subset. </p>
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<h3>5.What is the difference between proper and improper subsets?</h3>
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<p>The proper subsets are a set that doesn’t include the set itself, and improper subsets include the set itself. </p>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>