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Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (aRb) if and only if (a+b) is divisible by (3). Choose the correct classification.
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if and only if (a^2+b^2=0). Choose the correct statement.
Class 12 · Mathematics · Hard
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)}). Which property fails?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4,5}), (aRb) if and only if (a-b) is divisible by (3). What is the equivalence class of (2)?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), the relation (R={(a,b):a+b) is a perfect square(}) is given. Choose the correct classification.
Class 12 · Mathematics · Hard
→On (A={1,2,3,4,5,6}), (aRb) if and only if both (a) and (b) are divisible by (2), or both are not divisible by (2). Choose the correct conclusion.
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if and only if (a-b=1). What type of relation is it?
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if and only if (|a-b|<1). Choose the correct statement.
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R) is an equivalence relation. If (1R2) and (3) is not related to any other distinct element, which classes are possible?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R) is an equivalence relation. If (1R2) and (2R4), which conclusion is necessary?
Class 12 · Mathematics · Hard
→On (A={1,2,3}), (R) is to be an equivalence relation and ((1,2)\in R). Which pair must necessarily be in (R)?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4,5}), (aRb) if and only if (a-b) is divisible by (2). What is the equivalence class of (3)?
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if and only if (ab\ge0). What type of relation is it?
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if and only if (ab>0). Choose the correct classification.
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (aRb) if and only if both (a) and (b) are less than (3). Choose the correct statement.
Class 12 · Mathematics · Hard
→Which relation on A={1,2,3} is symmetric but not transitive?
Class 12 · Mathematics · Hard
→Which relation on (A={1,2,3,4}) is reflexive only, but neither symmetric nor transitive?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (aRb) if and only if (a=b) or (a+b=5). What are the equivalence classes?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (aRb) if and only if (a=b) or ({a,b}={1,2}). What type of relation is it?
Class 12 · Mathematics · Hard
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