The set is usually represented by the capital letter. In Mathematics, a set is defined as the collection of well-defined distinct objects. We saw that this is the case with the first two questions because we had sets that are equivalent, but not equal. Why or why not? All other trademarks and copyrights are the property of their respective owners. And it is not necessary that they have same elements, or they are a subset of each other. When we have two sets that have the exact same elements, we call them equal sets. Therefore, if two sets have the same cardinality, they are equivalent! That makes them equivalent sets! Also, the order doesn’t matter for the elements in a set. If P = {1, 3, 9, 5, −7} and Q = {5, −7, 3, 1, 9,}, then P = Q. However, the set of things that Jamie bought is equivalent to the set of things that Grace bought, because they each bought 6 things total, so the two sets each have the same number of things in them. Laura received her Master's degree in Pure Mathematics from Michigan State University. Set C and Set D both comprise word elements in completely different categories (Set C comprises articles of clothing you would wear when cold, and Set D comprises types of fruit), but they both have the same amount of elements, which is four. Sets are collections of numbers, letters, words, or pictures. Laura and Tristyn both have $4. Based on your answers to these questions, do you think that all equivalent sets are also equal sets? Here are some examples of equal sets: An equivalent set is simply a set with an equal number of elements. Your email address will not be published. Questions: Jamie and Grace go shopping. 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The cardinality of Set A is 4. and career path that can help you find the school that's right for you. just create an account. Also if two sets are the subsets of each other, they are said to be equal. Two sets are equal if all their elements are sameExample:A = {1, 2, 3, 4, 5}B = {3, 4, 5, 1, 2}Since A and B have the same elements.A and B are equal sets.A = … So, to rephrase in terms of cardinal number, we can say that: If A = B, then n(A) = n(B) and for any x ∈ A, x ∈ B too. Your email address will not be published. Jamie buys 2 shirts, 1 pair of shoes, and 3 pairs of pants. To be equivalent, the sets should have the same cardinality. For e.g. As a member, you'll also get unlimited access to over 83,000 If we want to write that two sets are equivalent, we would use the tilde (~) sign. credit by exam that is accepted by over 1,500 colleges and universities. Here are some examples of sets: When a set continues on for infinity, the last element in the set is followed by three dots known as an ellipsis, which indicates that the numbers continue. For each of the following groups of sets, determine whether they form a partition for the set of integers. What is the equivalence class of (1,2), i.e., [(1,2)]? Why or why not? We can have a set containing numbers, words, or even pictures. Explain. Why or why not? Required fields are marked *. We use a picture in this example to illustrate that sets don't have to contain elements that are letters, numbers, or words. Plus, get practice tests, quizzes, and personalized coaching to help you - History, Types & Examples, Glencoe Math Course: Online Textbook Help, McDougal Littell Pre-Algebra: Online Textbook Help, Algebra Connections: Online Textbook Help, Ohio End of Course Exam - Integrated Math II: Test Prep & Practice, TExES Mathematics 7-12 (235): Practice & Study Guide, GED Math: Quantitative, Arithmetic & Algebraic Problem Solving, Holt McDougal Algebra 2: Online Textbook Help. Explain your answer. Some sets contain images. Two sets are equivalent if they have the same cardinality or the same number of elements. Why or why not? Two sets are equal if they contain the same elements. Already registered? We would write this as: Set A ~ Set B. This is represented by: If the condition discussed above is not met, then the sets are said to be unequal. 's' : ''}}. They are indicated with brackets: { }. Study.com has thousands of articles about every It does not matter what order the elements are in. 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Other trademarks and copyrights are the subsets of each other therefore, if two sets a and B can written!