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Cardinality

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

MathematicsLet N={1,2,3,...}. If U={x∈N:x≤20} and A={x∈U:x is a perfect square}, what is the value of |A'|?Class 10SetsComplement of a Set and Its PropertiesLevel 9Medium MathematicsIf U is the set of all lowercase English letters and V = {a, e, i, o, u}, how many elements does the complement V' contain?Class 10SetsComplement of a Set and Its PropertiesLevel 9Easy MathematicsIf A = {0, 1, 2, 3, 4}, how many elements of the power set P(A) contain 0 and have odd cardinality?Class 10SetsPower Set and SubsetsLevel 9Medium MathematicsIf |A| = 7, how many elements of the power set P(A) have at least 6 elements?Class 10SetsPower Set and SubsetsLevel 9Medium MathematicsIf A = {p, q, r}, how many non-empty proper subsets does A have?Class 10SetsPower Set and SubsetsLevel 9Medium MathematicsIf P(A) has 256 elements, how many elements are in P(P(A))?Class 10SetsPower Set and SubsetsLevel 10Hard MathematicsIf |A| = 6, how many elements of P(A) have cardinality 2 or cardinality 4?Class 10SetsPower Set and SubsetsLevel 10Hard MathematicsIf A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is the value of |P(A ∩ B)|, where P denotes the power set?Class 10SetsPower Set and SubsetsLevel 10Medium MathematicsIf \(A=\{x,y,z,w\}\), how many elements of \(\mathcal{P}(A)\) are disjoint from \(\{x,z\}\)?Class 10SetsPower Set and SubsetsLevel 8Medium MathematicsIf \(A=\{1,2,3\}\), how many elements does \(\mathcal{P}(A)\setminus\{\varnothing,A\}\) contain?Class 10SetsPower Set and SubsetsLevel 8Medium MathematicsIf \(A=\{1,2,3,4,5\}\), how many subsets of the power set \(\mathcal{P}(A)\) have even cardinality?Class 10SetsPower Set and SubsetsLevel 8Hard MathematicsIf A={a,b,c,d}, how many elements of P(A) are subsets with an odd number of elements?Class 10SetsPower Set and SubsetsLevel 10Medium MathematicsIf |U| = 15 and |A'| = 6, what is |A|?Class 10SetsComplement of a Set and Its PropertiesLevel 10Easy MathematicsIf |U| = 20, |A| = 12, |B| = 9, and |A ∩ B| = 5, what is |(A ∪ B)'|?Class 10SetsComplement of a Set and Its PropertiesLevel 10Medium MathematicsLet U = {x ∈ Z | −3 ≤ x ≤ 4} and A = {x ∈ U | x² < 4}. How many elements are in the complement A′ of A with respect to U?Class 10SetsComplement of a Set and Its PropertiesLevel 10Medium MathematicsIf |P(A)| = 128, what is the value of |A|?Class 10SetsPower Set and SubsetsLevel 10Medium MathematicsIf U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {2, 4, 6, 8}, what is n(P(A'))?Class 10SetsPower Set and SubsetsLevel 10Medium MathematicsIf A = {1, 2, 3}, how many elements of the power set P(A) contain at least one element?Class 10SetsPower Set and SubsetsLevel 10Easy MathematicsIf A = {2, 4, 6} and B = {6, 8, 10}, how many elements does the power set P(A ∪ B) have?Class 10SetsPower Set and SubsetsLevel 10Medium MathematicsIf A = {g, h, i, j}, how many elements of P(A) are also proper subsets of A?Class 10SetsPower Set and SubsetsLevel 10Easy