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
In three sets, only A = 19, only B = 23, only C = 17, only A ∩ B = 8, only B ∩ C = 10, only C ∩ A = 6, and A ∩ B ∩ C = 5. What is n(B ∪ C)?If n(A ∪ B) = 126, n(A − B) = 47, and n(B − A) = 39, what is n(A ∩ B)?If A ⊆ B, n(A) = 38, n(B) = 91, and n(U) = 130, what is n(Bᶜ)?Let \(U=\{1,2,3,\ldots,30\}\), \(A=\{x:x\text{ is a multiple of }2\}\), and \(B=\{x:x\text{ is a multiple of }3\}\). What is \(n(A\cap B)\)?Let \(U=\{1,2,3,\ldots,40\}\), \(A=\{x:x\text{ is divisible by }4\}\), and \(B=\{x:x\text{ is divisible by }5\}\). What is \(n(A\cup B)\)?Let U = {1, 2, 3, ..., 50}, A be the set of prime numbers, and B be the set of even numbers. What is A ∩ B?Let \(U=\{1,2,3,\ldots,60\}\), \(A=\{x:x\text{ is divisible by }2\}\), \(B=\{x:x\text{ is divisible by }3\}\), and \(C=\{x:x\text{ is divisible by }5\}\). What is \(n(A\cap B\cap C)\)?Given n(A − B) = 34, n(B − C) = 41, and n(C − A) = 29, which conclusion cannot always be assumed to be true?If n(A) = 48, n(B) = 52, n(A − B) = 17, and n(B − A) = 21, what is n(A ∩ B)?If n(A ∪ B ∪ C) = 128, 63 elements are in exactly one set, and 11 are in all three sets, how many elements are in exactly two sets?In a Venn diagram, what set is (A ∩ B) ∪ (A ∩ Bᶜ) equal to?If A and B are two overlapping circles in a Venn diagram, what is A − (A ∩ B) equal to?If A ⊆ B ⊆ C, n(C) = 132, n(B) = 84, and n(A) = 37, what is n(C − A)?If n(A) = 94, n(A ∩ B) = 40, n(A ∩ C) = 37, and n(A ∩ B ∩ C) = 16, how many elements belong only to A?U = {1, 2, 3, ..., 36}, A = {x : x is divisible by 2}, and B = {x : x is divisible by 3}. What is n(A ∩ B)?In U = {1, 2, 3, ..., 70}, A is the set of prime numbers and B is the set of even numbers. What is A ∩ B?If only n(A − B) = 42, n(B − C) = 35, and n(C − A) = 31 are given, which conclusion cannot always be assumed true?If n(A ∪ B) = 139, n(A) = 82, n(B) = 76, and n(U) = 190, what is n(Aᶜ ∪ Bᶜ)?If A and B are two overlapping sets, what is A − (A ∩ B) equal to?If n(A ∩ B) = 45, n(A ∩ C) = 38, n(B ∩ C) = 35, and n(A ∩ B ∩ C) = 16, how many elements are in exactly two sets?