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Questions and Answers
Which of the following sets is the empty set?
Which of the following sets is the empty set?
How many proper subsets can be formed from the set A = { 1, 2, 3, 4, 5 }?
How many proper subsets can be formed from the set A = { 1, 2, 3, 4, 5 }?
What is the solution set for the equation x² - 4x + 3 = 0?
What is the solution set for the equation x² - 4x + 3 = 0?
What is the cardinality of set { x: x is an integer and 2 < x < 3 }?
What is the cardinality of set { x: x is an integer and 2 < x < 3 }?
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Study Notes
Empty Set Identification
- The empty set is represented by the symbol Φ.
- Among the given options, {Φ} is considered a set containing an empty set; it is not empty itself.
- Option D, { x: x is an integer and 2 < x < 3 }, does not contain any integers, hence it is the empty set.
Proper Subsets of Set A
- A proper subset is a subset that does not include all the elements of the original set.
- For a set A with n elements, the total number of subsets is 2^n.
- Given A = {1, 2, 3, 4, 5}, it has 5 elements.
- Total subsets of A = 2^5 = 32.
- To find the number of proper subsets, subtract one (the full set itself) from the total: 32 - 1 = 31.
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Description
Test your knowledge of set theory and proper subsets in this Class XI Mathematics quiz. With a focus on identifying empty sets and calculating proper subsets, this quiz is designed to challenge your understanding of these fundamental concepts. Answer the questions to see how well you grasp these mathematical ideas!
