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 A ∩ B = A ∪ B ∪ C, which conclusion about C must be true?If A = {1, 2, 3}, B = {3, 4}, and C = {2, 3, 5}, what is (A ∪ B) \ C?If |A ∪ B| = 70, |A \ B| = 25, and |B \ A| = 30, what is |A ∩ B|?If A \ B ⊆ C and A ∩ B ⊆ C, which conclusion is necessarily true?If A ∪ B = U and A \ B = ∅, what must be true about B?For sets A, B, and C, consider the identity (A \ B) ∩ C = A ∩ (C \ B). Which statement is correct?If A = [-2, 5] and B = (1, 7], what is A \ B?If U = {1, 2, ..., 90}, A = {x ∈ U : 6 divides x}, and B = {x ∈ U : 15 divides x}, what is |A ∪ B|?Which statement is always true for all sets A, B, and C?In a class of 120 students, 72 are in the mathematics set M, 64 are in the physics set P, and 28 are in both sets. How many students are in neither M nor P?If U = {1, 2, ..., 84}, A = {x ∈ U : 7 divides x}, and B = {x ∈ U : 12 divides x}, what is |A ∪ B|?If A = [-4, 6) and B = (-1, 8], what is A \ B?If A ∪ B = U, A ∩ B = C, and C ⊆ A, then A \ B is equal to which set?If |A \ B| = 17, |B \ A| = 23, and |A ∩ B| = 14, what is |A ∪ B|?If A ∩ (B ∪ C) = A, which conclusion must be true?If A = {2, 4, 6, 8, 10, 12}, B = {3, 6, 9, 12, 15}, and C = {6, 12, 18}, what is (A ∪ B) ∩ C?If |A| = 41, |B| = 36, and |A \ B| = 19, what is |A ∪ B|?If A △ B = (A \ B) ∪ (B \ A), |A △ B| = 34, and |A ∪ B| = 51, what is |A ∩ B|?If A ⊆ B and C ⊆ D, which inclusion must be true?If A ∪ B = A and A \ B = ∅, which conclusion is correct?