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Class 12 · Mathematics · Hard
→When will the relation (R={(a,b):d(a,b)=2}) be symmetric, where (d) is a distance function?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R={(a,b):a+2b\text{ is even}}). Is (R) symmetric?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R={(a,b):a^2+b^2\text{ is even}}). Which statement is correct about (R)?
Class 12 · Mathematics · Hard
→If (R) is a symmetric relation, what is (R\cup R^{-1}) equal to?
Class 12 · Mathematics · Hard
→If (R) is a symmetric relation, what is (R\cap R^{-1}) equal to?
Class 12 · Mathematics · Hard
→In which relation is (R) symmetric but not reflexive?
Class 12 · Mathematics · Hard
→How many symmetric relations are there on a set with (5) elements?
Class 12 · Mathematics · Hard
→If (A) has (4) elements, how many symmetric relations are not reflexive?
Class 12 · Mathematics · Hard
→A directed graph has arrows (1\to2), (2\to1), (2\to3), and no other arrows. What must be added to make it symmetric?
Class 12 · Mathematics · Hard
→If the directed graph of a relation shows a reverse arrow for every arrow, what type of relation is it?
Class 12 · Mathematics · Hard
→Which example is symmetric but not transitive?
Class 12 · Mathematics · Hard
→For (R={(a,b):a+b\text{ is even}}) on (A={1,2,3,4}), which statement is correct?
Class 12 · Mathematics · Hard
→For the same relation (R={(a,b):a+b\text{ is odd}}) on (A={1,2,3,4}), which statement is correct?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R={(a,b):a+b\text{ is odd}}). How many ordered pairs are in (R)?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4,5}), (R={(a,b):a+b=6}). How many pairs are in (R), and is it symmetric?
Class 12 · Mathematics · Hard
→Which condition most clearly gives a symmetric relation?
Class 12 · Mathematics · Hard
→If (R) is symmetric and ((q,p)\notin R), what conclusion is correct about ((p,q))?
Class 12 · Mathematics · Hard
→If (R) is symmetric and ((p,q)\notin R), which conclusion is always correct?
Class 12 · Mathematics · Hard
→Which statement is correct about the identity relation (I_A={(a,a):a\in A})?
Class 12 · Mathematics · Hard
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