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 \(A\cup(B\cap C)=(A\cup B)\cap(A\cup C)\), which law is this?If \(A\cup(A\cap B)=A\), which law of sets does this represent?If \(A\cap(A\cup B)=A\), which law of sets does this represent?With respect to the universal set \(U\), which of the following sets is equal to \(A\cap B'\)?If \(A\subseteq B\subseteq C\), then what is \(A\cap(C\setminus B)\)?If \(A\cap B\ne\varnothing\) and \(A\setminus B=\varnothing\), which conclusion is correct?If \(n(A)=18\), \(n(B)=25\), and \(n(A\cup B)=25\), then what is \(n(A\setminus B)\)?If \(A=\{x\in\mathbb{R}\mid 0\le x<5\}\) and \(B=\{x\in\mathbb{R}\mid 3<x\le 8\}\), what is \((A\cup B)\setminus(A\cap B)\)?If \(n(A\cup B\cup C)=86\), \(n(A)=38\), \(n(B)=34\), \(n(C)=31\), \(n(A\cap B)=12\), \(n(B\cap C)=10\), and \(n(C\cap A)=9\), what is the value of \(n(A\cap B\cap C)\)?If \(U=\{1,2,\ldots,40\}\), \(A=\{x:x\in U,\ 2\mid x\}\), \(B=\{x:x\in U,\ 3\mid x\}\), and \(C=\{x:x\in U,\ 5\mid x\}\), then what is \(n(A\cup B\cup C)\)?If \(n(A\cup B)=70\), \(n(A\setminus B)=22\), and \(n(B\setminus A)=31\), then what is \(n(A\cap B)\)?If \(U=\{1,2,\ldots,30\}\), \(A=\{x:x\in U,\ 2\mid x\}\) and \(B=\{x:x\in U,\ 3\mid x\}\), what is \(n(A\cup B)\)?If \(A\subseteq B\), then \((A\cup B)\setminus(A\cap B)\) is equal to which set?If \(A\setminus B=\varnothing\) and \(B\setminus A=\varnothing\), which conclusion is correct?If \(A\cap B=A\cup B\), what is the correct statement about A and B?If A = {x : x² − 5x + 6 = 0} and B = {x : x² − 4x + 3 = 0}, what is A ∩ B?If \(A=(-2,5]\) and \(B=[1,8)\), what is \(A\setminus B\)?If A = (-∞, 2] and B = (0, ∞), then what is (A ∩ B) ∪ (A \ B)?If n(A) = 18, n(B) = 22, and n(A ∪ B) = 31, what is n(A \ B)?If A △ B = (A \ B) ∪ (B \ A), A = {1, 2, 4, 6}, and B = {2, 3, 4, 5}, what is A △ B?