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) ∪ (B − A), where A = {a, b, c, d} and B = {b, d, e, f}, find A △ B.If A ∩ B = A ∩ C and A ∪ B = A ∪ C, which conclusion is correct?If A = {x ∈ ℝ : 0 ≤ x < 3} and B = {x ∈ ℝ : 1 < x ≤ 5}, what is A ∪ B?If A = {x ∈ ℝ : −3 ≤ x ≤ 2} and B = {x ∈ ℝ : −1 < x < 4}, what is A − B?If n(A − B) = 12, n(B − A) = 9, and n(A ∩ B) = 7, what is n(A ∪ B)?If n(A) = 52, n(B) = 47, n(A ∩ B) = 21, and n(U) = 80, what is n((A ∪ B)')?If two sets A and B are disjoint, where n(A) = 15 and n(B) = 19, what is n(A ∪ B)?If A ∪ B = A, which statement about B is correct?If \(A\cap B=B\), which conclusion is correct?If \(A=\{1,3,5,7,9\}\), \(B=\{2,3,5,8,9\}\), and \(C=\{3,4,5,9\}\), what is \(A\cap B\cap C\)?If \(A=\{x\in\mathbb{N}:x\le 20,\ x\text{ is prime}\}\) and \(B=\{x\in\mathbb{N}:x<20,\ x\text{ is odd}\}\), what is \(A-B\)?If \(A=\{x:x=2k,\ k\in\mathbb{Z}\}\) and \(B=\{x:x=4k,\ k\in\mathbb{Z}\}\), which relation is correct?If \(A\) is the set of distinct letters in the English word MATHEMATICS and \(B\) is the set of distinct letters in the English word STATISTICS, what is \(A\cap B\)?If \(A\cap(B-C)=\varnothing\), what does this mean?If \(A=\{1,2,3,4\}\), what are \(A\cup\varnothing\), \(A\cap\varnothing\), and \(A-\varnothing\), respectively?If \(A\cup B=U\) and \(A\cap B=\varnothing\), then which set is equal to \(B\)?If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,2,8,9\}\), find \((A-B)\cup(A-C)\).If \(A=\{2,3,5,7,11,13\}\) and \(B=\{x\in A:x>5\}\), find \(A\cap B\).If \(A=\{x\in\mathbb{Z}: |x|\le 3\}\) and \(B=\{x\in\mathbb{Z}: x^2-2x\le 0\}\), find \(A\cap B\).If \(A=\{x\in\mathbb{N}:x\mid36\}\) and \(B=\{x\in\mathbb{N}:x\mid48\}\), what is \(A\cap B\)?