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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: A. K = {4, 9, 25}
Explanation: A positive integer has exactly three positive divisors precisely when it is the square of a prime: if x = p², its divisors are 1, p, and p². The prime squares less than 40 are 2² = 4, 3² = 9, and 5² = 25. The next prime square, 7² = 49, is not less than 40. Hence K = {4, 9, 25}.
Correct answer: A. A = {-4, -3, -2, -1, 0, 1, 4}
Explanation: The inequality x² ≤ 16 gives -4 ≤ x ≤ 4, so the integer candidates are -4, -3, -2, -1, 0, 1, 2, 3, and 4. Among these, the only prime numbers are 2 and 3. Removing them leaves -4, -3, -2, -1, 0, 1, and 4. Negative integers, zero, and one are not prime by the definition of a prime number.
Correct answer: B. 8
Explanation: The positive multiples of 6 below 40 are 6, 12, 18, 24, 30, and 36. The positive multiples of 9 below 40 are 9, 18, 27, and 36. Taking the union gives {6, 9, 12, 18, 24, 27, 30, 36}, which has 8 elements. The common multiples 18 and 36 are counted only once because a set has no repeated elements.
Correct answer: A. 40
Explanation: The set A consists of the part only in A and the common part. Therefore, n(A ∩ B) = n(A) − n(A − B) = 58 − 21 = 37. Then n(A ∪ B) = 58 + 49 − 37 = 70. The complement contains the elements of U outside this union, so n((A ∪ B)′) = 110 − 70 = 40. Option A is correct.
