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Class 12 · Mathematics
→For a non-empty set (A), which statement is always true about the identity relation?
Class 12 · Mathematics
→On (A={1,2,3,4}), (aRb) if and only if (|a-b|=2). What type of relation is it?
Class 12 · Mathematics
→On (A={1,2,3}), (R={(1,2),(2,3),(1,3)}). Choose the correct statement.
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(3,4),(4,3)}). Which property fails immediately?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,4),(4,2),(1,4),(4,1)}). Choose the correct statement.
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if and only if (a) is less than (b). Choose the correct classification.
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if and only if (a) is less than or equal to (b). Choose the correct conclusion.
Class 12 · Mathematics
→On (A={1,2,3,4}), (aRb) if and only if (a+b) is divisible by (4). What type of relation is it?
Class 12 · Mathematics
→On real numbers, (aRb) if and only if (a^2\le b^2). Choose the correct statement.
Class 12 · Mathematics
→On real numbers, (aRb) if and only if (a^3=b^3). What type of relation is it?
Class 12 · Mathematics
→On (A={1,2,3,4}), (aRb) if and only if (a\le b) and (b-a\le2). Is it transitive?
Class 12 · Mathematics
→On (A={1,2,3,4}), (aRb) if and only if (a\le b) and (b-a\le2). Which property definitely fails?
Class 12 · Mathematics
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)}). What is the correct conclusion?
Class 12 · Mathematics
→On a set A with four elements, how many relations are both reflexive and antisymmetric?
Class 12 · Mathematics
→If (A) has (4) elements, how many symmetric relations can be formed on (A)?
Class 12 · Mathematics
→If (A) has (5) elements, how many reflexive relations can be formed on (A)?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) have the same remainder when divided by (3). What are the equivalence classes?
Class 12 · Mathematics
→On (A={1,2,3,4}), (aRb) if and only if both (a) and (b) are even. What type of relation is it?
Class 12 · Mathematics
→On real numbers, (aRb) if and only if (a-b) is irrational. Choose the correct classification.
Class 12 · Mathematics
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