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 = {x : x² − 5x + 6 = 0} and B = {x : x² − 4x + 3 = 0}, what is A ∩ B?If \(A=(-2,5]\) and \(B=[1,8)\), what is \(A\setminus B\)?If A = (-∞, 2] and B = (0, ∞), then what is (A ∩ B) ∪ (A \ B)?If n(A) = 18, n(B) = 22, and n(A ∪ B) = 31, what is n(A \ B)?If A △ B = (A \ B) ∪ (B \ A), A = {1, 2, 4, 6}, and B = {2, 3, 4, 5}, what is A △ B?If A ∪ B = A, which statement is definitely true?If A \ (B ∪ C) is to be written using only intersection and set difference, which form is correct?If A \ (B ∩ C) is simplified, which option is correct?If A = {1, 2, 3, 4, 5}, B = {2, 4, 6}, and C = {1, 4, 7}, what is (A ∪ B) ∩ C?If A = {a, b, c, d}, B = {b, d, e}, and C = {d, e, f}, what is (A \ B) ∪ (B ∩ C)?If A ⊆ C and B ⊆ C, what is (A ∪ B) \ C?If A ∩ B = ∅, n(A) = p, and n(B) = q, what is n(A ∪ B)?In a class of 40 students, 24 chose Mathematics and 18 chose Physics, while 7 chose neither subject. How many students chose both subjects?Let U = {1, 2, ..., 20}, A = {x ∈ U : x is prime}, and B = {x ∈ U : x is odd}. What is A \ B?If A = {x ∈ Z : −3 ≤ x < 4} and B = {x ∈ Z : x² ≤ 4}, what is A \ B?If A = {x ∈ R : x < 2} and B = {x ∈ R : x > −1}, what is A ∪ B?In what context is the statement A \ B = A ∩ B′ correct?If A − B means A \ B, which statement is generally false?If A \ B = A, which conclusion is definite?If A = {(x, y) : x, y ∈ {1, 2, 3}, x < y} and B = {(x, y) : x + y = 4}, what is A ∩ B?