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
Let U = {1, 2, ..., 30}. If A is the set of multiples of 2 in U and B is the set of multiples of 5 in U, what is n(A ∪ B)?Let U = {1, 2, ..., 50}. If A is the set of multiples of 4 in U and B is the set of multiples of 6 in U, what is n(A ∩ B)?If n(A ∪ B) = 84 and n(A ∩ B) = 27, what is n(A − B) + n(B − A)?Out of 70 students, 45 study Hindi, 40 study English, and 30 study both languages. How many students study at least one of the two languages?If n(U) = 60, n(A) = 35, and n(B) = 32, what is the minimum possible value of n(A ∩ B)?If n(U) = 100, n(A) = 64, and n(B) = 58, what is the minimum possible value of n(A ∪ B)?If n(A) = 46 and n(B) = 39, what is the maximum possible value of n(A ∩ B)?If n(A) = 30, n(B) = 28, and n(A ∪ B) = 52, what is n(A − B)?If n(A − B) = 18, n(B − C) = 25, and n(C − A) = 20, can n(A ∪ B ∪ C) be determined uniquely from only these data?In a Venn diagram, n(A ∩ B) = 14 and n(A ∩ B ∩ C) = 6. How many elements are only in A ∩ B?In a class of 95 students, 56 study Mathematics, 49 study Science, and 27 study both subjects. How many students study exactly one subject?If n(A) = 64, n(B) = 59, and n(A ∪ B) = 91, what is n(A △ B)?If A ⊆ B, n(B) = 83, n(A) = 47, and n(U) = 120, what is n(B − A)?If A ∩ B = ∅, n(A) = 44, n(B) = 52, and n(U) = 130, what is n((A ∪ B)′)?If n(A) = 5x + 4, n(B) = 4x + 7, n(A ∩ B) = 2x + 3, and n(A ∪ B) = 78, what is the value of x?If n(A − B) = 3x + 2, n(B − A) = 2x + 5, n(A ∩ B) = x + 4, and n(A ∪ B) = 71, what is x?Let U = {1, 2, ..., 72}. If A is the set of multiples of 6 and B is the set of multiples of 8, what is n(A ∩ B)?Let U = {1, 2, ..., 90}. If A is the set of multiples of 5 and B is the set of multiples of 9, what is n(A ∪ B)?If U = {1, 2, ..., 40}, A is the set of prime numbers and B is the set of even numbers, what is A ∩ B?If U = {1, 2, ..., 36}, A is the set of square numbers and B is the set of multiples of 3, what is n(A ∩ B)?