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Class 12 · Mathematics · Expert
→If (R) is a symmetric relation, which statement about (R\cup R^{-1}) is correct?
Class 12 · Mathematics · Expert
→If (R) and (S) are both symmetric relations, which statement about (R-S) is correct?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,5}), (R={(a,b):a+b\equiv0\pmod 3}). Which property does this relation satisfy?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4}), (R={(a,b):a+b) is odd(}). What type of relation is it?
Class 12 · Mathematics · Expert
→On real numbers, (aRb) iff (|a-b|<1). What type of relation is it?
Class 12 · Mathematics · Expert
→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 · Expert
→On (A={1,2,3}), how many relations are neither symmetric nor antisymmetric?
Class 12 · Mathematics · Expert
→If (A) has (4) elements, how many relations are reflexive and symmetric but not antisymmetric?
Class 12 · Mathematics · Expert
→If (A) has (3) elements, how many antisymmetric relations can be formed on (A)?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,5,6}), (R={(a,b):\gcd(a,b)=1}). Which property does this relation satisfy?
Class 12 · Mathematics · Expert
→On (A={1,2,3}), how many relations are both symmetric and antisymmetric but not reflexive?
Class 12 · Mathematics · Expert
→On (A={1,2,3}), how many symmetric relations are not reflexive?
Class 12 · Mathematics · Expert
→On (A={1,2,3}), how many reflexive relations are not symmetric?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4}), how many symmetric relations contain exactly two diagonal pairs?
Class 12 · Mathematics · Expert
→If (A) has (4) elements, how many relations on (A) are both irreflexive and antisymmetric?
Class 12 · Mathematics · Expert
→If (A) has (n) elements, what is the number of relations on (A) that are both symmetric and irreflexive?
Class 12 · Mathematics · Expert
→If (R) is a relation on a set (A), when will (R^{-1}) be symmetric?
Class 12 · Mathematics · Expert
→On (A={1,2,3}), starting from (R={(1,2),(2,3)}), how many pairs will the smallest relation containing (R) and being reflexive, symmetric and transitive have?
Class 12 · Mathematics · Expert
→On real numbers, (aRb) iff (a^2+b^2=0). What type of relation is it?
Class 12 · Mathematics · Expert
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