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 ∈ R : x ≠ 0} and B = {x ∈ R : x² > 0}, what is A △ B?If A and B are finite sets and n(A ∪ B) = n(A) + n(B), which conclusion is correct?If \(A=\{x\in\mathbb{R}:x\ge 2\}\), \(B=\{x\in\mathbb{R}:x<6\}\), and \(C=\{x\in\mathbb{R}:x=4\}\), what is \((A\cap B)-C\)?If n(A ∪ B ∪ C) = 88, n(A − B) = 19, n(B − A) = 24, n(A ∩ B) = 13, and C − (A ∪ B) has 32 elements, what is n((A ∪ B) − C) if C has no element of A ∪ B?If A = {x ∈ ℤ : −7 ≤ x ≤ 7}, B = {x ∈ ℤ : x² ≤ 16}, and C = {x ∈ ℤ : 3 divides x}, what is (A − B) ∩ C?If A = {x ∈ ℝ : −3 ≤ x < 5}, B = {x ∈ ℝ : 1 < x ≤ 8}, and C = {x ∈ ℝ : x ≤ 2}, what is (A ∪ B) ∩ C?For a universal set U with n(U) = 110, if n(A) = 64, n(B) = 57, and n(A ∩ B) = 29, what is n((A ∪ B)′)?If A ⊆ B and C ∩ B = ∅, then (A ∪ C) ∩ B is equal to which set?If n(A) = 42, n(B) = 35, and n(A ∪ B) = 60, what is n(A ∩ B)?If n(A − B) = 28 and n(A ∩ B) = 16, what is n(A)?If \(A=\{x\in\mathbb{Z}:-3\le x\le 5\}\) and \(B=\{x\in\mathbb{Z}:x^2\le 9\}\), what is \(A\setminus B\)?If A = [−2, 4] and B = (1, 6), what is A ∩ B?If A = (−∞, 3] and B = [1, ∞), what is A ∪ B?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 \(U=\{1,2,\ldots,20\}\), \(A=\{x:x\in U,\ x\text{ is even}\}\), and \(B=\{x:x\in U,\ x\text{ is divisible by }3\}\), then what is \(n((A\cup B)')\)?If \(A\subseteq B\), then what is \(A\cup(B\setminus A)\) equal to?If \(A\cap B=A\) and \(A\cup B=B\), which of the following is the correct conclusion?If \(n(A)=30\), \(n(B)=24\), and \(n(A\setminus B)=18\), what is the value of \(n(A\cup B)\)?If \(A\cup B=A\cap B\), which of the following conclusions is always true?Assume that \(\mathbb{N}=\{1,2,3,\ldots\}\). If \(A=\{x\in\mathbb{N}\mid x\le 12\}\) and \(B=\{x\in\mathbb{N}\mid x\text{ is prime}\}\), with \(B\) restricted to \(A\), what is \(A\setminus B\)?