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Class 11 · Mathematics · Hard
→If A = {1,3,5}, B = {2,3,4,5}, and C = {3,5,7}, what is A × (B − C)?
Class 11 · Mathematics · Hard
→If \(A=\{0,1,2\}\), \(B=\{1,2,3,4\}\), and \(C=\{2,4,6\}\), what is the value of \(|A\times(B\cap C)|\)?
Class 11 · Mathematics · Hard
→If \(A=\{1,2,3,4\}\), \(B=\{2,4,6\}\), and \(C=\{4,6,8\}\), what is the value of \(|A\times(B\cup C)|\)?
Class 11 · Mathematics · Hard
→If (|A|=3) and (|B|=5), what is the number of possible relations from (A) to (B)?
Class 11 · Mathematics · Hard
→If (|A|=4), (|B|=5), and (R\subseteq A\times B), in how many ways can (R) have exactly (2) elements?
Class 11 · Mathematics · Hard
→If (A={2,4,6,8}) and (B={2,4,6}), how many pairs ((a,b)) in (A\times B) satisfy (\gcd(a,b)=2)?
Class 11 · Mathematics · Hard
→If A = {2,3,4} and B = {6,8,9,12}, how many pairs (a,b) in A × B have a dividing b?
Class 11 · Mathematics · Hard
→If (A={1,2,3,4,5}) and (B={1,4,9,16,25}), how many pairs ((a,b)) in (A\times B) satisfy (b=a^2)?
Class 11 · Mathematics · Hard
→If A = {1,2,3,4,5,6} and B = {1,2,3}, how many pairs (a,b) in A × B satisfy a ≥ 2b + 1?
Class 11 · Mathematics · Hard
→If (A={0,1,2,3,4}) and (B={2,3,4,5}), how many pairs ((a,b)) in (A\times B) satisfy (a<b)?
Class 11 · Mathematics · Hard
→If \(A=\{1,2,3,4,5\}\) and \(B=\{2,4,6\}\), how many ordered pairs \((a,b)\) in \(A\times B\) satisfy \(a+b=9\)?
Class 11 · Mathematics · Hard
→If \(A=\{a,b\}\) and \(B=\{1,2,3,4\}\), how many ordered pairs are there in \(B\times A\)?
Class 11 · Mathematics · Hard
→If (A={1,2}), (B={3,4,5}), and (C={6,7}), what is (|A\times B\times C|)?
Class 11 · Mathematics · Hard
→Assume that \(\mathbb{N}=\{1,2,3,\ldots\}\). If \(A=\{x\in\mathbb{N}:3\le x\le 8\}\) and \(B=\{y\in\mathbb{N}:y\le 4\}\), what is the value of \(|A\times B|\)?
Class 11 · Mathematics · Hard
→If (A={3,5,7}) and (B={2,4,6}), which ordered pair in (A\times B) has first component (7) and second component (4)?
Class 11 · Mathematics · Hard
→If (A={1,2,3,4}), (B={2,3,4,5,6}), and (R={(a,b):b\ge a+2}), how many elements are in (R\subseteq A\times B)?
Class 11 · Mathematics · Hard
→If (A={1,2,3,4,5}) and (B={1,2,3,4}), how many pairs ((a,b)) in (A\times B) have (a+b) divisible by (4)?
Class 11 · Mathematics · Medium
→If A = {1,2,3}, B = {1,2,3,4}, and S = {(a,b) : b > a + 1} ⊆ A × B, how many elements are in S?
Class 11 · Mathematics · Hard
→If A = {1, 2, 3, 4, 5} and B = {2, 3, 4, 5}, how many ordered pairs (a, b) in A × B have a + b divisible by 2?
Class 11 · Mathematics · Hard
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