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Operations On Sets Union Intersection Difference

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf \(U=\{1,2,\ldots,30\}\), \(A=\{x:x\in U,\ 2\mid x\}\) and \(B=\{x:x\in U,\ 3\mid x\}\), what is \(n(A\cup B)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 16MediumMathematicsIf \(n(A\cup B)=70\), \(n(A\setminus B)=22\), and \(n(B\setminus A)=31\), then what is \(n(A\cap B)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(U=\{1,2,\ldots,40\}\), \(A=\{x:x\in U,\ 2\mid x\}\), \(B=\{x:x\in U,\ 3\mid x\}\), and \(C=\{x:x\in U,\ 5\mid x\}\), then what is \(n(A\cup B\cup C)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(n(A\cup B\cup C)=86\), \(n(A)=38\), \(n(B)=34\), \(n(C)=31\), \(n(A\cap B)=12\), \(n(B\cap C)=10\), and \(n(C\cap A)=9\), what is the value of \(n(A\cap B\cap C)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(A=\{x\in\mathbb{R}\mid 0\le x<5\}\) and \(B=\{x\in\mathbb{R}\mid 3<x\le 8\}\), what is \((A\cup B)\setminus(A\cap B)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(n(A)=18\), \(n(B)=25\), and \(n(A\cup B)=25\), then what is \(n(A\setminus B)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(A\cap B\ne\varnothing\) and \(A\setminus B=\varnothing\), which conclusion is correct?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(A\subseteq B\subseteq C\), then what is \(A\cap(C\setminus B)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsWith respect to the universal set \(U\), which of the following sets is equal to \(A\cap B'\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(A\cap(A\cup B)=A\), which law of sets does this represent?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(A\cup(A\cap B)=A\), which law of sets does this represent?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(A\cup(B\cap C)=(A\cup B)\cap(A\cup C)\), which law is this?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(A\cap(B\cup C)=(A\cap B)\cup(A\cap C)\), which law is this?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3,5,7\}\), and \(C=\{3,4,5,8\}\), what is \((A\setminus B)\cap C\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(A\) and \(B\) are finite sets, which is the correct formula for \(n(A\setminus B)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf \(A\) and \(B\) are subsets of the universal set \(U\), what is the complement of \(A\setminus B\) with respect to \(U\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf A = {a, b, c, d} and B = {c, d, e}, how many elements does P(A ∩ B) contain?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf A △ B is defined as (A \ B) ∪ (B \ A), and n(A ∪ B) = 40 and n(A ∩ B) = 13, what is n(A △ B)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsIf A = {x ∈ Z : |x| ≤ 4} and B = {x ∈ Z : x² − 2x − 3 = 0}, how many elements does A \ B contain?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18MediumMathematicsLet \(U=\{1,2,\ldots,50\}\), \(A=\{x:x\in U,\ 4\mid x\}\), and \(B=\{x:x\in U,\ 6\mid x\}\). What is \(n(A\cap B)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 18Medium