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Class 12 · Mathematics · Hard
→On (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) have the same parity. What are its equivalence classes?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (aRb) if and only if (a) and (b) have the same remainder when divided by (2). What type of relation is it?
Class 12 · Mathematics · Hard
→Which of the following relations on (A={1,2,3}) is an equivalence relation?
Class 12 · Mathematics · Hard
→If a relation is reflexive and transitive, is it always symmetric? Choose the correct option.
Class 12 · Mathematics · Hard
→If a relation is reflexive and symmetric, is it always transitive? Choose the correct option.
Class 12 · Mathematics · Hard
→If a relation is symmetric and transitive, is it always reflexive? Choose the correct option.
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,4),(4,3)}). What type of relation is it?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (aRb) if and only if (a-b) is divisible by (2). Choose the correct statement.
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (aRb) if and only if (a+b\le 5). What type of relation is it?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (aRb) if and only if (a\neq b). Choose the correct classification.
Class 12 · Mathematics · Hard
→On a set of people, (aRb) if and only if (a) is taller than (b). What type of relation is it?
Class 12 · Mathematics · Hard
→On a set of students, (aRb) if and only if (a) and (b) have the same birth month. What type of relation is it?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(1,3),(3,4),(1,4),(2,4)}). Choose the correct statement.
Class 12 · Mathematics · Hard
→On (A={1,2,3,4,6}), (aRb) if and only if (a) divides (b). What is the correct property of this relation?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (aRb) if and only if the greatest common divisor of (a) and (b) is (1). Choose the correct statement.
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if and only if (a-b>0). Choose the correct statement.
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if and only if (|a|=|b|). What type of relation is it?
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if and only if (a^2=b^2). Choose the correct type.
Class 12 · Mathematics · Hard
→On real numbers, (aRb) if and only if (a-b) is rational. What type of relation is it?
Class 12 · Mathematics · Hard
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