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Class 11 · Mathematics
→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
→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
→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
→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
→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
→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
→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 (3) and (a\ne b)?
Class 11 · Mathematics
→If (A={0,1,2,3,4}) and (B={0,1,2,3,4}), how many pairs ((a,b)) in (A\times B) satisfy (a+b\le4) and (a\ne b)?
Class 11 · Mathematics
→If A={1,2,3,4}, B={1,2,3,4}, and U=A×B, how many ordered pairs (a,b) in U satisfy a<b or a+b=5?
Class 11 · Mathematics
→If A={1,2,3,4,5}, B={1,2,3,4,5}, and T={(a,b): |a−b|≤2}, what is |T|?
Class 11 · Mathematics
→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 (\operatorname{lcm}(a,b)=6)?
Class 11 · Mathematics
→If \(A=\{1,2,3,4\}\), \(B=\{1,2,3\}\), and \(C=\{0,1\}\), how many ordered triples \((a,b,c)\) in \(A\times B\times C\) satisfy \(a=b+c\)?
Class 11 · Mathematics
→If (A={1,2,3,4}) and (B={2,3,5,7,11}), how many pairs ((a,b)) in (A\times B) have (b-a) prime?
Class 11 · Mathematics
→If (A={1,2,3,4}) and (B={1,2,3,4,5,6}), how many pairs ((a,b)) in (A\times B) satisfy (ab\le12) and (a+b) is odd?
Class 11 · Mathematics
→If A={1,2,3,4,5} and B={1,2,3,4,5}, how many ordered pairs (a,b) in A×B satisfy a+b=6 or a=b?
Class 11 · Mathematics
→If \(A=\{1,2,3\}\), \(B=\{1,2,3,4\}\), and \(C=\{2,3,5\}\), what is the value of \(\lvert A\times(B\setminus C)\rvert+\lvert(A\times B)\cap(A\times C)\rvert\)?
Class 11 · Mathematics
→If A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, and R = {(a,b): b/a ∈ N}, what is |R|?
Class 11 · Mathematics
→If (A={1,2,3,4,5}) and (B={1,2,3,4,5}), how many pairs ((a,b)) in (A\times B) satisfy (\gcd(a,b)=1) and (a+b) even?
Class 11 · Mathematics
→If (A={0,1,2,3}), (B={0,1,2,3,4}), and (R={(a,b):b\ge a^2-1}), what is (|R|)?
Class 11 · Mathematics
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