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Subjects

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 U = {1, 2, …, 60}, A = {x ∈ U : 2 divides x}, and B = {x ∈ U : 3 divides x}, what is |A ∪ B|?If A ∪ B = A ∩ B, which conclusion about A and B is correct?If |A| = 28, |B| = 35, and |A ∪ B| = 50, what is |A \ B|?If A \ B = A, which statement must be true?If A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}, and C = {1, 4, 7, 8}, what is (A ∪ B) ∩ C?If A ⊆ B, then A ∪ (B \ A) is equal to which set?If A ∩ (B \ C) = ∅, which inclusion must be true?If A = {x ∈ ℤ : −3 ≤ x ≤ 4} and B = {x ∈ ℤ : x² < 10}, what is A \ B?If |A| = 12, |B| = 18, |C| = 20, |A ∩ B| = 5, |B ∩ C| = 7, |C ∩ A| = 4, and |A ∩ B ∩ C| = 2, what is |A ∪ B ∪ C|?If A ∩ B = A and A ∪ B = B, which relation between A and B is correct?If A = {2, 3, 5, 7, 11} and B = {x ∈ A | x + 1 ∈ A}, what is A \ B?If A \ (B ∪ C) is described using only the meaning of A, B, C, ∩, and set difference, which elements does it contain?If A = {1, 2, 4, 8, 16}, B = {2, 4, 6, 8, 10}, and C = {4, 8, 12, 16}, what is (A ∩ C) \ B?If A △ B = (A \ B) ∪ (B \ A), |A| = 21, |B| = 19, and |A ∩ B| = 8, what is |A △ B|?If (A ∪ B) \ (A ∩ B) = ∅, what is true about A and B?If A \ B = B \ A, which conclusion is correct?Which identity correctly rewrites \(A\cap(B\cup C)\)?If \(A=\{x\in\mathbb{N}:x\le 20,\ x\text{ is prime}\}\) and \(B=\{x\in\mathbb{N}:x\le 20,\ x\text{ is odd}\}\), what is \(A\setminus B\)?If \(A\subseteq C\) and \(B\subseteq C\), what is \((A\cup B)\setminus C\)?If \(U=\{1,2,\ldots,100\}\), \(A=\{x\in U:4\mid x\}\), and \(B=\{x\in U:10\mid x\}\), what is \(|A\cap B|\)?