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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 \(A=\{1,2,3,4,5,6,7,8\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,2,3,4\}\), what is \(B\setminus C\)?If \(A=\{1,4,7,10\}\), \(B=\{2,4,8,10\}\), and \(C=\{4,10,12\}\), what is \((A\cup B)\cap C\)?If \(A=\{p,q,r,s,t\}\), \(B=\{q,s,u\}\), and \(C=\{r,s,t,u\}\), what is \(A\setminus(B\cap C)\)?If \(A=\{1,2,3,4\}\) and \(B=\{2,4,6,8\}\), which statement about \(A\setminus B\subseteq A\) is correct?If \(A=\{x:x\in\mathbb{N},\ 1\le x\le 10\}\), \(B=\{1,4,7,10\}\), and \(C=\{2,4,6,8,10\}\), what is \(A\setminus(B\cup C)\)?If \(A=\{x:x\in\mathbb{N},\ x\mid 30\}\) and \(B=\{x:x\in\mathbb{N},\ x\mid 45\}\), what is \((A\cup B)\setminus(A\cap B)\)?If A = {1,2,3,4,5,6,7,8}, B = {2,4,6,8,10}, and C = {1,4,8,12}, what is (A ∩ B) \ C?In a survey, 58 students take online classes, 46 students visit the library, and 21 do both. How many students do exactly one activity?If A \ B = ∅ and B \ A = ∅, which conclusion is correct?Let A = {x ∈ Z : -5 < x < 4}, and let B contain the even integers satisfying -5 < x < 4. What is A \ B?If P = {a,b,c,d} and Q = {b,d,e}, find P ∩ Q.If A = {2,4,6,8,10} and B = {1,2,3,4}, what is B \ A?If A = {1,2,3,4}, B = {3,4,5}, and C = {4,5,6}, what is (A ∪ B) ∩ C?If A = {1,3,5,7,9}, B = {2,3,5,8}, and C = {3,4,5,6}, what is A − (B ∩ C)?If n(A) = 18, n(B) = 14, and n(A ∩ B) = 6, what is n(A ∪ B)?If n(A ∪ B) = 45, n(A) = 28, and n(B) = 25, find n(A ∩ B).In a class, 30 students study Mathematics, 22 students study Physics, and 12 students study both subjects. How many students study at least one subject?If A = {x : x ∈ ℤ, −2 ≤ x ≤ 4} and B = {x : x ∈ ℤ, x is odd}, what is A ∩ B?If A = [1, 5] and B = [3, 8], what is the interval A ∩ B?If A = (2, 7) and B = [5, 9], what is A ∪ B?