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Class 11 · Mathematics · Expert
→If (A={1,2,3,4,5,6}) and (B={1,2,3,4,5,6}), how many pairs ((a,b)) in (A\times B) satisfy (\gcd(a,b)=2)?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4,5}), (B={1,2,3,4,5}), and (R={(a,b):a+b=6}), how many pairs are in (R\circ R)?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4}) and (B={1,2,3,4,5,6,7,8}), how many pairs ((a,b)) in (A\times B) satisfy (a\mid b) but not (b\mid a)?
Class 11 · Mathematics · Expert
→If \(A=\{0,1,2,3,4\}\), \(B=\{0,1,2,3,4\}\), and \(R=\{(a,b)\in A\times B: a^2\equiv b\pmod{5}\}\), what is the value of \(|R|\)?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4,5,6}) and (B={1,2,3,4,5,6}), how many pairs ((a,b)) in (A\times B) have (a+b) divisible by (5)?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4,5}) and (B={1,2,3,4,5}), how many pairs ((a,b)) in (A\times B) have (a+b) divisible by (4)?
Class 11 · Mathematics · Expert
→If (A={1,2,3}), (B={1,2,3}), and (C={1,2,3}), how many triples ((a,b,c)) in (A\times B\times C) satisfy (a+b+c=6)?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4}), (B={1,2,3,4}), and (R=A\times B), what is the minimum number of pairs to remove from (R) so that no pair ((a,a)) remains?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4,5}), (B={0,1,2,3,4}), and (R={(a,b):a-b\in{1,3}}), what is (|R|)?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4,5,6}) and (B={1,2,3,4,5,6}), how many pairs ((a,b)) in (A\times B) have both (a) and (b) prime or both composite?
Class 11 · Mathematics · Expert
→If A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5, 6}, and R = {(a, b) ∈ A × B : b = 2a or b = 3a}, what is the value of |R|?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4,5}) and (B={1,2,3,4,5}), how many pairs ((a,b)) in (A\times B) satisfy (a<b) and (a+b) is even?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4}), (B={1,2,3,4}), and (R={(a,b):a+b\text{ is odd}}), what is the number of subsets of (R)?
Class 11 · Mathematics · Hard
→If A={1,2,3,4,5,6} and B={1,2,3,4,5,6}, how many ordered pairs (a,b) in A×B satisfy a+b=ab?
Class 11 · Mathematics · Expert
→If \(A=\{1,2,3,4,5\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b):a+b\le6\}\), how many ordered pairs in \(R\) have an even first component \(a\)?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4}) and (B={0,1,2,3,4,5}), how many pairs ((a,b)) in (A\times B) satisfy (b\equiv a^2\pmod{5})?
Class 11 · Mathematics · Expert
→If \(A=\{1,2,3\}\) and \(B=\{1,2,3,4,5,6\}\), how many ordered pairs \((a,b)\) in \(A\times B\) satisfy that \(b\) is a multiple of \(a\) and \(b\ne a\)?
Class 11 · Mathematics · Expert
→If A={1,2,3,4,5}, B={1,2,3,4,5}, and R={(a,b): a+b=7}, which of the following ordered pairs must belong to R⁻¹?
Class 11 · Mathematics · Expert
→If A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}, and R = {(a, b) : a² < b}, how many ordered pairs are in R, that is, what is |R|?
Class 11 · Mathematics · Expert
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