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 \(A\cup B=A\cap B\), what conclusion follows?If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), how many elements are there in the power set \(\mathcal{P}(A-B)\)?If \(n(A\cup B)=75\), \(n(A-B)=28\), and \(n(B-A)=31\), what is \(n(A\cap B)\)?If \(A=\{1,2,3,4,5,6,7,8\}\) and \(B=\{2,4,6,8,10\}\), what is \((A\cup B)-(A\cap B)\)?If \(A\cap B=\varnothing\), then which set is \(A-(A-B)\) equal to?Which of the following expressions is equivalent to \(A\cap(B\cup C)\)?Which of the following sets is equivalent to \(A\cup(B\cap C)\)?If \(A=\{x\in\mathbb{N}:x\le 15\}\), \(B=\{x\in\mathbb{N}:3\mid x\}\), and \(C=\{x\in\mathbb{N}:5\mid x\}\), where \(\mathbb{N}=\{1,2,3,\ldots\}\), what is \(A\cap(B\cup C)\)?If \(A=\{x\in\mathbb{N}:x\le30,\ 2\mid x\}\) and \(B=\{x\in\mathbb{N}:x\le30,\ 3\mid x\}\), what is \(A\cap B\)?If A = {1, 2, 3, 4, 5}, B = {2, 3, 6}, and C = {3, 4, 7}, what is the value of A − (B ∩ C)?If A, B, and C are sets such that A − B = A − C and A ∩ B = A ∩ C, which statement is correct with respect to A?If n(A) = 40, n(B) = 36, n(C) = 28, n(A ∩ B) = 14, n(B ∩ C) = 10, n(C ∩ A) = 12, and n(A ∩ B ∩ C) = 5, then what is n((A ∪ B ∪ C) − C)?If A = {x ∈ R : -2 < x ≤ 6}, B = {x ∈ R : 1 ≤ x < 8}, and C = {x ∈ R : 4 < x ≤ 10}, what is (A ∪ C) − B?If A, B, and C are sets, then A ∩ (B − C) is equal to which expression?If A = {x ∈ Z : -4 ≤ x ≤ 6}, B = {x ∈ Z : x² ≤ 16}, and C = {x ∈ Z : 2 divides x}, what is (A ∩ B) − C?If A ∪ B = {2,4,6,8,10,12,14}, A − B = {2,10}, and B − A = {6,14}, what is A ∩ B?If n(A) = 58, n(B) = 44, and n(A − B) = 23, what is n(A ∪ B)?If A = {x ∈ R : x² − 5x + 6 ≤ 0} and B = {x ∈ R : x < 4}, what is the difference set A − B?If A = {x ∈ R : |x − 2| ≤ 3} and B = {x ∈ R : x² ≤ 4}, what is A ∩ B?If A ⊆ U, B ⊆ U, and A − B = A ∩ B′, then (A − B) ∪ (A ∩ B) is equal to which of the following?