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Complement Of A Set And Its Properties

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf \(U=\{1,2,\ldots,64\}\) and \(A=\{x:x=2^n,\ n\in\mathbb N,\ 1\le n\le6\}\), what is the cardinality \(|A'|\) of the complement of \(A\) in \(U\)?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf \(U=\{1,2,\ldots,32\}\), \(A=\{x:x\text{ is a multiple of }4\}\), and \(B=\{x:x\text{ is a multiple of }16\}\), how many elements are in \(A'\cup B\)?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf \(U'=\varnothing\), which statement about \(U\) is correct?Class 10SetsComplement of a Set and Its PropertiesLevel 21Easy MathematicsIf U = ℝ, A = {x : −2 < x ≤ 4} and B = {x : 1 ≤ x < 7}, what is A′ ∪ B′?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf U = {1, 2, …, 20}, A = {1, 4, 9, 16} and B = {3, 6, 9, 12, 15, 18}, what is A ∩ B′?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf \(U=\{1,2,\ldots,84\}\), \(A=\{x:x\text{ is divisible by }12\}\), and \(B=\{x:x\text{ is divisible by }21\}\), what is \(|(A\cap B)'|\)?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf \((A\cup B')\cap(A'\cup B')=B'\), which simplification shows it correctly?Class 10SetsComplement of a Set and Its PropertiesLevel 21Hard MathematicsIf \(A'\cap B'=A'\), which of the following conclusions is always true?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsFor subsets \(A\) and \(B\) of a universal set \(U\), if \(A\subseteq B\), which relation between their complements is always true?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf U = {1, 2, ..., 30}, A = {x : x is even}, and B = {x : x is prime}, what is |A' ∩ B'|?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf A Δ B denotes the symmetric difference of A and B, what does (A Δ B)' represent?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf U = {1, 2, …, 144} and A = {x : x is not divisible by 12}, what is |A′|?Class 10SetsComplement of a Set and Its PropertiesLevel 10Easy MathematicsIf U = {1, 2, ..., 18}, A = {2, 4, 6, 8, 10, 12}, and B = {6, 9, 12, 15, 18}, what is (B − A)'?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf U = R and A = {x : x² − 4x − 12 < 0}, what is A'?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf U = {1, 2, …, 24} and A′ = {1, 5, 7, 11, 13, 17, 19, 23}, how many elements are in A?Class 10SetsComplement of a Set and Its PropertiesLevel 10Easy MathematicsIf U = {1, 2, ..., 70}, A = {x : x is divisible by 5}, and B = {x : x is divisible by 7}, what is |A' ∩ B|?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf U ≠ ∅, which statement cannot always be true?Class 10SetsComplement of a Set and Its PropertiesLevel 21Easy MathematicsIf the universal set is U = R and A = (-∞, -1) ∪ [3, 8), what is A'?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf the universal set is U = {1, 2, ..., 42}, A = {x ∈ U : x is divisible by 3}, and B = {x ∈ U : x is divisible by 7}, what is |A' ∪ B'|?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf |U| = 90, |A ∩ B| = 24, |A′ ∩ B| = 17, and |A′ ∩ B′| = 29, what is |A ∩ B′|?Class 10SetsComplement of a Set and Its PropertiesLevel 21Hard