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 \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), 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?If \(A\) and \(B\) are sets such that \(A\cap B=\varnothing\), what is the value of \((A\cup B)\setminus B\)?If \(n(U)=120\), \(n(A)=70\), \(n(B)=65\), and \(n(A\cap B)=40\), what is the value of \(n(A'\cap B')\)?If \(A=\{1,2,4,8,16\}\), \(B=\{1,3,9,27\}\), and \(C=\{1,5,25\}\), what is \((A\cap B)\cup(B\cap C)\cup(C\cap A)\)?If \(A=\{x\in\mathbb{Z}\mid -3\le x\le 8\}\), \(B=\{x\in\mathbb{Z}\mid 0\le x\le 5\}\), and \(C=\{x\in\mathbb{Z}\mid x\text{ is even}\}\), what is \((A\setminus B)\cap C\)?If \(A=\{x\in\mathbb{N}:x\le 10\}\), \(B=\{x\in\mathbb{N}:x\text{ is odd}\}\), and \(C=\{x\in\mathbb{N}:x\text{ is prime}\}\), what is \(A\cap(B\setminus C)\)?If \(A\cup B=A\cup C\) and \(A\cap B=A\cap C\), which of the following is correct?If \(A=\{x\in\mathbb{R}:x^2-4x+3>0\}\) and \(B=\{x\in\mathbb{R}:x>1\}\), what is \(A\cap B\)?If \(A=\{x\in\mathbb{R}:x^2\le 9\}\) and \(B=\{x\in\mathbb{R}:x^2<1\}\), what is \(A\setminus B\)?If \(A=\{1,2,3\}\) and \(B=\{2,3,4,5\}\), how many elements does \(\mathcal{P}(A\cup B)\) contain?If \(A=\{1,2,3,4,5,6\}\) and \(B=\{2,4,6\}\), what is \(n(\mathcal{P}(A\setminus B))\)?If n(A − B) = 17, n(B − C) = 22, and B − C has 6 elements common with A, what is n((A − B) ∪ (B − C))?If A, B, and C satisfy A ⊆ B ⊆ C, then (C − A) − (B − A) is equal to which set?If \(A\cap B=B\cap C=C\cap A=\varnothing\), \(n(A)=12\), \(n(B)=15\), and \(n(C)=18\), what is the value of \(n(A\cup B\cup C)\)?If \(A=\{x\in\mathbb{N}:x\le 30,\ x\text{ is a perfect square}\}\) and \(B=\{x\in\mathbb{N}:x\le 30,\ 3\mid x\}\), what is \(A-B\)?Which of the following set identities is true for all sets A, B, and C?