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 \(A=\{1,2,3,4,5,6,7\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,4,7,8\}\), what is the value of \((A\cup B)\cap C\)?If \(A-B=\{p,q\}\), \(A\cap B=\{r,s,t\}\), and \(B-A=\{u\}\), what is the value of \(n(A)\)?If \(A\cap B=\varnothing\) and \(A\cup B=A\cup C\), which additional condition is sufficient for \(B\subseteq C\)?If \(A=\{x\in\mathbb{N}:x\le 40,\ 4\mid x\}\) and \(B=\{x\in\mathbb{N}:x\le 40,\ 6\mid x\}\), what is \(A\cap B\)?If \(A=\{x\in\mathbb{N}:x\mid 72\}\) and \(B=\{x\in\mathbb{N}:x\mid 90\}\), what is \(A\cap B\)?If \(A=\{1,2,3,4,5\}\), \(B=\{3,4,5,6\}\), and \(C=\{5,6,7\}\), what is the value of \((A-B)\cup(B-C)\)?Which option is equal to \((A\cup B)-A\)?If \(A\cap B=A\) and \(B\cap C=B\), which conclusion is correct?If \(A=\{x\in\mathbb{Z}:x^2-1=0\}\) and \(B=\{x\in\mathbb{Z}:x^2=1\}\), what is \(A-B\)?Which of the following statements is always true for sets?If A = {x : x is a letter of the English word ALGEBRA} and B = {x : x is a letter of the English word GEOMETRY}, what is A ∪ B?If \(A=\{x\in\mathbb{N}:x\le25,\ x\text{ is prime}\}\) and \(B=\{x\in\mathbb{N}:x\le25,\ x\text{ is odd}\}\), what is \(B-A\)?If U = {1, 2, ..., 20}, A = {x ∈ U : 2 divides x}, and B = {x ∈ U : 5 divides x}, what is (A ∪ B)'?If A = {x ∈ R : x ≤ 1} and B = {x ∈ R : x > −2}, what is A ∩ B?If A ∪ B = B and A ∩ C = C, which statement must be true?If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), and \(C=\{1,3,5\}\), what is the value of \((A-B)\cap C\)?If \(A=\{x\in\mathbb{Z}:-6\le x\le 6\}\) and \(B=\{x\in\mathbb{Z}:x^2<10\}\), what is \(A-B\)?If A △ B = (A − B) ∪ (B − A), n(A △ B) = 26, and n(A ∩ B) = 9, what is n(A ∪ B)?If A − B = ∅ and B − C = ∅, which conclusion is correct?If A = {x ∈ R : 1 ≤ x ≤ 9} and B = {x ∈ R : 3 < x < 7}, what is A − B?