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Class 12 · Mathematics · Hard
→If (R) is a relation and (R^{-1}=R), which conclusion is definite?
Class 12 · Mathematics · Hard
→If (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), why is (R) not a partial order relation?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), if (aRb) when (a+b) is odd, which statement about (R) is correct?
Class 12 · Mathematics · Hard
→If (A) has (3) elements, what is the number of reflexive and antisymmetric relations on (A)?
Class 12 · Mathematics · Hard
→If (A) has (3) elements, how many relations on (A) are both symmetric and antisymmetric?
Class 12 · Mathematics · Hard
→If (A) has (3) elements, how many relations on (A) are both reflexive and symmetric?
Class 12 · Mathematics · Hard
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(1,3)}). Is this relation antisymmetric?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R={(a,b):a+b=5}). Which property does this relation satisfy?
Class 12 · Mathematics · Hard
→For (R={(1,2)}) on (A={1,2,3}), which minimum pair must be added to make it symmetric?
Class 12 · Mathematics · Hard
→If (R) and (S) are symmetric relations on (A), which statement about (R\cup S) is correct?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R={(a,b):a-b) is odd(}). What type of relation is it?
Class 12 · Mathematics · Hard
→If (A) has (n) elements, which formula gives the number of relations that are both reflexive and symmetric on (A)?
Class 12 · Mathematics · Hard
→If (A) has (n) elements, which formula gives the number of symmetric relations on (A)?
Class 12 · Mathematics · Hard
→On (A={1,2,3}), (R={(1,2),(2,1),(2,3),(3,2)}). Which property does this relation satisfy?
Class 12 · Mathematics · Hard
→If a relation is both symmetric and antisymmetric, what is true about its off-diagonal pairs?
Class 12 · Mathematics · Hard
→How many relations on (A={1,2,3}) are both reflexive and symmetric?
Class 12 · Mathematics · Hard
→How many symmetric relations are there on (A={1,2,3})?
Class 12 · Mathematics · Medium
→If (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), why is (R) not antisymmetric?
Class 12 · Mathematics · Medium
→If (R={(1,1),(2,2),(3,3),(1,2)}) on (A={1,2,3}), is (R) antisymmetric?
Class 12 · Mathematics · Medium
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