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Subjects

Mathematics

Operations on Sets (Union, Intersection, Difference)

समुच्चयों पर संक्रियाएँ (संघ, प्रतिच्छेद और अंतर)

In Class 11 Mathematics, the Sets chapter introduces Operations on Sets (Union, Intersection, Difference). Students learn to combine sets using union, identify common elements through intersection, and find elements belonging to one set but not another using difference. They also apply these operations to subset relations, Venn diagrams, and problems involving the number of elements in sets.

Practice questions

If n(U) = 75, n(A) = 46, and n(B) = 41, what is the minimum possible value of n(A ∩ B)?If n(A) = 73 and n(B) = 58, what is the maximum possible value of n(A ∩ B)?If n(U) = 150, n(A) = 91, and n(B) = 86, what is the minimum possible value of n(A ∪ B)?If n(A) = 42, n(B) = 38, and n(A ∩ B) = 17, what is n(A' ∩ B)?If n(A) = 55, n(B) = 62, and n(A − B) = 23, what is n(A ∪ B)?If n(A ∪ B) = 98 and n(A ∩ B) = 35, what is the value of n(A − B) + n(B − A)?If A ⊆ B, then what is (A ∪ B) − A equal to?If A ∩ B = ∅, then what is A − B equal to?If (n(A\cup B)=n(A)), which conclusion is correct according to the Venn diagram?If n(A ∩ B) = 0, n(A) = 28, and n(B) = 34, what is n(A △ B)?In a survey of 120 people, 66 read a newspaper, 58 read a magazine, and 24 read neither. How many read both?In an exam, 82 students solved question A, 76 solved B, 69 solved C, 37 solved both A and B, 32 solved both B and C, 29 solved both C and A, and 15 solved all three. How many solved at least one question?If n(A ∩ B) = 26 and n(A ∩ B ∩ C) = 10, how many elements are only in A ∩ B?If only n(A−B)=20, n(B−C)=18, and n(C−A)=16 are given, can n(A ∪ B ∪ C) be determined uniquely?If n(A) = 72, n(B) = 67, and n(A ∪ B) = 101, what is n(A △ B), the number of elements in the symmetric difference of A and B?If n(A) = 6x + 5, n(B) = 5x + 9, n(A ∩ B) = 3x + 4 and n(A ∪ B) = 106, then what is the value of x?If n(A − B) = 4x + 1, n(B − A) = 3x + 6, n(A ∩ B) = 2x + 5 and n(A ∪ B) = 120, then what is x?Let U = {1, 2, ..., 96}. If A is the set of multiples of 6 in U and B is the set of multiples of 10 in U, what is n(A ∪ B)?If U = {1, 2, ..., 105}, A is the set of multiples of 7 and B is the set of multiples of 15, what is n(A ∩ B)?If U = {1, 2, ..., 50}, A is the set of prime numbers and B is the set of multiples of 5, what is A ∩ B?