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Class 12 · Mathematics · Hard
→On a family of sets, (A,R,B) if (A\subseteq B). What type of relation is (R)?
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if (a-b\ge 0). What type of relation is it?
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if (a=b+1). Is this relation transitive?
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if (a^2=b^2). What type of relation is (R)?
Class 12 · Mathematics · Hard
→On natural numbers, (aRb) if (a) is a factor of (b). What type of relation is it?
Class 12 · Mathematics · Hard
→If (R={(1,2),(2,4),(1,4),(4,2)}), (R) is not transitive because which pair is required?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R={(1,2),(2,2),(2,4),(1,4),(4,4),(3,3)}). Choose the correct statement.
Class 12 · Mathematics · Hard
→If (R={(1,1),(1,2),(2,2),(2,3),(1,3),(3,3)}), what type will (R^{-1}) be?
Class 12 · Mathematics · Hard
→If (R) is transitive, which statement is correct about (R^{-1})?
Class 12 · Mathematics · Hard
→If (R={(1,2)}) and (S={(2,3)}), both are transitive individually. What about (R\cup S)?
Class 12 · Mathematics · Hard
→Is the union (R\cup S) of two transitive relations always transitive?
Class 12 · Mathematics · Hard
→If (R) and (S) are both transitive relations on a set (A), what is correct about (R\cap S)?
Class 12 · Mathematics · Hard
→If (R) is transitive and ((2,5)\in R), ((5,8)\in R), ((8,11)\in R), which pair must definitely be in (R)?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R={(1,2),(2,4),(4,3),(1,4),(2,3)}). (R) is not transitive because which pair is missing?
Class 12 · Mathematics · Hard
→On integers, (aRb) if (a \equiv b \pmod{5}). Which statement is correct about (R)?
Class 12 · Mathematics · Hard
→If (R={(1,2),(2,3),(3,1)}), which group must start getting added to form the full transitive closure?
Class 12 · Mathematics · Hard
→Which relation on A={1,2,3} is transitive but not reflexive?
Class 12 · Mathematics · Hard
→In a relation like the previous one, what is the correct conclusion when every required pair is actually present?
Class 12 · Mathematics · Hard
→On (A={1,2,3}), (R={(1,1),(1,2),(2,2),(2,1),(2,3),(1,3)}). Is (R) transitive?
Class 12 · Mathematics · Hard
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