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SubjectsMathematics
समुच्चय और उनके निरूपण
In this Class 10 Mathematics topic from the chapter “Sets,” students learn how to describe and represent a collection of well-defined objects using clear mathematical language. They explore common forms such as descriptive statements, roster or tabular notation, and set-builder notation, while identifying elements and understanding the symbols used for membership and non-membership. The topic builds accuracy in reading, writing, comparing, and interpreting sets, providing a foundation for later ideas involving relationships and operations on sets.
Correct answer: B. B
Explanation: The relation A ⊆ B means that every element of A is already an element of B. The union A ∪ B contains all elements that belong to A or B. Since A contributes no element outside B, taking the union adds nothing to B. Therefore, A ∪ B = B. Notice that A ∩ B = A, but the question asks for the union, so option B is correct.
Correct answer: A. {L, E, V}
Explanation: The governing concept is that a set contains distinct elements, so repetition does not create new members. The letters in LEVEL are L, E, V, E, L; after removing repeated occurrences, the membership list is {L, E, V}. Therefore option A is correct. Options B and D treat a set like an ordered list or multiset by repeating letters, while C incorrectly omits E.
Correct answer: A. {−2, −1, 0, 1}
Explanation: The notation specifies that x must be an integer and must satisfy −2 ≤ x < 2. The symbol ≤ includes −2, while the symbol < excludes 2. Listing all integers in this half-closed interval gives −2, −1, 0, and 1. Therefore A = {−2, −1, 0, 1}, which is exactly option A. Option B omits −2, option C incorrectly includes 2, and option D omits valid integers and includes an invalid endpoint.
Correct answer: B. It contains all elements under consideration
Explanation: A universal set is the set that contains every object or element being considered in a particular problem or discussion. It is usually denoted by U. Its elements depend on the stated context; therefore, it need not be empty, infinite, or restricted to numbers. For example, if the discussion concerns English vowels, U may be the set of all vowels. Hence option B is correct.
Correct answer: A. \(\{1,2,3\}\)
Explanation: In a set, the order in which elements are written does not matter, and repeated elements are counted only once. Thus \(A\) and \(B\) contain exactly the same elements: 1, 2, and 3. Their union therefore contains these three distinct elements only: \(A\cup B=\{1,2,3\}\). No element such as 4 or 6 can be added because it appears in neither set.
Correct answer: C. 3
Explanation: The condition says that the second coordinate is one more than the first, so \(y=x+1\). Substituting each element of \(A\) gives \(1,3,5\) for \(x=0,2,4\), respectively. Every resulting value belongs to \(B\), producing the pairs \((0,1),(2,3),(4,5)\). Thus there are exactly 3 pairs, and option C is correct.
