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 \(A\setminus B=\varnothing\) and \(B\setminus A=\varnothing\), what is the relation between \(A\) and \(B\)?Which expression is equal to \(A\setminus(B\cap C)\)?Which expression is equal to \(A\setminus(B\cup C)\)?If \(n(A\cup B)=75\), \(n(A\cap B)=18\), and \(n(A)=46\), what is the value of \(n(B)\)?In a class of 64 students, 38 study Mathematics, 32 study Physics, and 20 study both subjects. How many students study exactly one subject?In a survey of 90 people, 52 like tea, 47 like coffee, and 19 like both tea and coffee. How many people like neither tea nor coffee?If U = {1, 2, ..., 30}, A = {x : x ∈ U, 2 divides x}, and B = {x : x ∈ U, 5 divides x}, then what is n(A \ B)?If A = {x ∈ R | x² − 5x + 6 = 0} and B = {x ∈ R | x² − 4x + 3 = 0}, what is A ∩ B?If A = {x ∈ R : x² ≤ 16} and B = {x ∈ R : x > 1}, what is the interval form of A ∩ B?If A = {x ∈ R : −1 < x ≤ 5} and B = {x ∈ R : 2 ≤ x < 7}, then what is A \ B?If A = {1, 2, 3, 4, 5}, B = {2, 4, 6}, and C = {1, 4, 7}, what is A ∩ (B ∪ C)?If A = {1, 3, 5, 7, 9}, B = {3, 6, 9}, and C = {1, 2, 3, 4}, what is (A ∪ B) \ C?If A ∩ B = ∅, n(A) = 21, and n(B) = 17, what is the value of n(A ∪ B)?If (A \ B = {2, 5}), (B \ A = {7}), and (A ∩ B = {1, 3}), then what is (A ∪ B)?If n(A \ B) = 12, n(B \ A) = 9, and n(A ∩ B) = 6, what is the value of n(A ∪ B)?If \(A\cup B=A\), what is the value of \(B\setminus A\)?If A ∩ B = B, which statement about A \ B is not definitely true?Let \(U=\{1,2,\ldots,50\}\), \(A=\{x:x\in U,\ 4\mid x\}\), and \(B=\{x:x\in U,\ 6\mid x\}\). What is \(n(A\cap B)\)?If A = {x ∈ Z : |x| ≤ 4} and B = {x ∈ Z : x² − 2x − 3 = 0}, how many elements does A \ B contain?If A △ B is defined as (A \ B) ∪ (B \ A), and n(A ∪ B) = 40 and n(A ∩ B) = 13, what is n(A △ B)?