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 \(A=\{x:x\text{ is a multiple of }4,\ 1\le x\le25\}\) and \(B=\{x:x\text{ is a multiple of }6,\ 1\le x\le25\}\), how many elements are in \(A\cup B\)?If \(A=\{x:x\in\mathbb N,\ x\le12\}\) and \(B=\{x:x\in\mathbb N,\ x\text{ is a perfect square},\ x\le12\}\), how many elements are in \(A-B\)?Which option is always true?Which statement is generally not true?If A = {1, 2, 3}, what is A ∪ ∅?If A = {1, 2, 3}, what is A ∩ ∅?If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is n(A − B) + n(B − A)?If n(A ∪ B) = 60, n(A − B) = 18, and n(B − A) = 22, what is n(A ∩ B)?If A = {x : x ∈ ℕ, x ≤ 15} and B = {x : x ∈ ℕ, x is odd, x ≤ 15}, what is A − B?In a group, 24 students study Hindi, 18 study English, and 7 study both languages. How many students study only Hindi?If A = [-1, 4] and B = (1, 6), what is A ∩ B?If A = {x : x² − 7x + 12 = 0} and B = {x : x² − 9x + 20 = 0}, what is A ∪ B?If A = {1, 4, 9, 16, 25} and B = {2, 4, 8, 16, 32}, what is (A − B) ∪ (B − A)?Let A = {x ∈ ℕ : 1 ≤ x ≤ 30 and x is a multiple of 2} and B = {x ∈ ℕ : 1 ≤ x ≤ 30 and x is a multiple of 3}. How many elements are in A ∩ B?If A = {x ∈ ℤ : −2 ≤ x < 5} and B = {x ∈ ℤ : x² ≤ 9}, then what is A − B?If A ∪ B = {1, 2, 3, 4, 5, 6}, A ∩ B = {2, 5}, and A − B = {1, 4}, what is B − A?If n(A) = 45, n(B) = 38, and n(A ∪ B) = 63, find n(A ∩ B).If A ⊆ B, which set is equal to (A ∪ B) − (A ∩ B)?If A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}, and C = {1, 4, 7, 8}, find A ∩ (B ∪ C).If A − B = ∅ and B − A ≠ ∅, which conclusion is correct?