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Class 12 · Mathematics
→On real numbers, (aRb) iff (a-b\in\mathbb{Q}). What is the equivalence class of (\sqrt{2})?
Class 12 · Mathematics
→On real numbers, (aRb) iff (a-b\in\mathbb{Z}) and (a+b\in\mathbb{Z}). What type of relation is it?
Class 12 · Mathematics
→On integers, (aRb) iff (a+2b) is divisible by (4). Which statement is correct?
Class 12 · Mathematics
→On integers, (aRb) iff (2a+3b) is divisible by (5). In which property does this relation fail?
Class 12 · Mathematics
→If (A={1,2,3,4}), how many equivalence relations have (1) and (2) in different classes?
Class 12 · Mathematics
→If (A={1,2,3,4}), how many equivalence relations have (1) and (2) in the same class?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), how many equivalence relations have exactly three equivalence classes?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), how many equivalence relations have exactly four equivalence classes?
Class 12 · Mathematics
→On (A={1,2,3}), how many relations are neither symmetric nor antisymmetric?
Class 12 · Mathematics
→On (A={1,2,3,4}), how many relations are reflexive and therefore cannot be irreflexive?
Class 12 · Mathematics
→If (A) has (4) elements, how many relations are reflexive and symmetric but not antisymmetric?
Class 12 · Mathematics
→If (A) has (3) elements, how many antisymmetric relations can be formed on (A)?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (R={(a,b):\gcd(a,b)=1}). Which property does this relation satisfy?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (R={(a,b):a+b) is divisible by (3)(}). How many pairs are in (R)?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(a,b):a+b\le 5}). How many pairs are in (R)?
Class 12 · Mathematics
→On (A={1,2,3}), how many relations are both symmetric and antisymmetric but not reflexive?
Class 12 · Mathematics
→On (A={1,2,3}), how many symmetric relations are not reflexive?
Class 12 · Mathematics
→On (A={1,2,3}), how many reflexive relations are not symmetric?
Class 12 · Mathematics
→On (A={1,2,3,4}), how many symmetric relations contain exactly two diagonal pairs?
Class 12 · Mathematics
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