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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 A ∩ B = A \ B, which conclusion about A is correct?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 10Medium MathematicsIf \(n(A\cup B)=n(A)+n(B)\) and \(n(A)=0\), what is \(A\cap B\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Easy MathematicsWhich expression is equal to \(A\setminus(B\setminus C)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Hard MathematicsIf \(A=\{x\in\mathbb Z:|x|\le 4\}\) and \(B=\{x\in\mathbb Z:x^2\le 9\}\), what is \(A\setminus B\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Medium MathematicsIf A \ B = A ∩ C and A ∩ B = A \ C, what is A ∩ B ∩ C?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 10Medium MathematicsIf \(A\cup B=A\cup C\), which additional statement is sufficient to prove \(B=C\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Hard MathematicsIf \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), what is \(\mathcal P(A\cap B)\cap\mathcal P(A\setminus B)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Hard MathematicsIf A ∩ B ⊆ C, which of the following sets must be empty?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 10Easy MathematicsIf \(A\setminus C=B\setminus C\) and \(A\cap C=B\cap C\), what is the conclusion about \(A\) and \(B\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Hard MathematicsIf \(A=\{1,3,5,7,9\}\), \(B=\{0,3,6,9\}\), and \(C=\{3,4,5,9\}\), what is \(A\cap(B\cup C)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Medium MathematicsIf \(A\cup B=A\) and \(A\cap B=B\), which of the following statements must be true?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Medium MathematicsIf A and B are finite sets and |A \ B| = 9, |B \ A| = 4, and |A ∩ B| = 11, what is |A ∪ B|?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 10Medium MathematicsIf A = {x ∈ ℝ | x² − 5x + 6 = 0} and B = {x ∈ ℝ | x² − 7x + 12 = 0}, what is A ∩ B?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 10Medium MathematicsIf \(A\setminus B=\{1,4\}\), \(A\cap B=\{2,3\}\), and \(B\setminus A=\{5,6,7\}\), what is \(A\cup B\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Medium MathematicsIf \(A\cap B=\varnothing\), which formula for \(|A\cup B|\) is correct?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Easy MathematicsIf \(A=\{a,b,c,d\}\) and \(B=\{b,d,e\}\), what is \((A\setminus B)\cup(B\setminus A)\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Medium MathematicsIf \(A\cup B=A\cup C\) and \(A\cap B=A\cap C\), which conclusion must be true?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Hard MathematicsIf \(U=\{1,2,\ldots,100\}\), \(A=\{x\in U:4\mid x\}\), and \(B=\{x\in U:10\mid x\}\), what is \(|A\cap B|\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Medium MathematicsIf \(A\subseteq C\) and \(B\subseteq C\), what is \((A\cup B)\setminus C\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Easy MathematicsIf \(A=\{x\in\mathbb{N}:x\le 20,\ x\text{ is prime}\}\) and \(B=\{x\in\mathbb{N}:x\le 20,\ x\text{ is odd}\}\), what is \(A\setminus B\)?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 17Easy