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Class 12 · Mathematics
→If (R) is an equivalence relation and ([a]\cap[b]\neq\varnothing), which statement is correct?
Class 12 · Mathematics
→On real numbers, (aRb) if and only if (a^2+b^2=1). Choose the correct classification.
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if and only if (a) and (b) have different remainders when divided by (2). What type of relation is it?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if and only if both (a,b) are odd or both are even. Choose the correct conclusion.
Class 12 · Mathematics
→Which relation on (A={1,2,3,4}) can have exactly two equivalence classes?
Class 12 · Mathematics
→How many equivalence relations can be formed on (A={1,2,3})?
Class 12 · Mathematics
→If (A={1,2,3,4,5}) and the sizes of equivalence classes are (2,2,1), how many ordered pairs are in the relation?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1)}). Which minimum pairs must be added to make it an equivalence relation?
Class 12 · Mathematics
→On real numbers, (aRb) if and only if (a-b\ge2). Choose the correct conclusion.
Class 12 · Mathematics
→On real numbers, (aRb) if and only if (a-b=2). Choose the correct classification.
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if and only if (|a-b|=2). Choose the correct statement.
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if and only if both (a,b) are less than (4) or (a=b). Choose the correct equivalence classes.
Class 12 · Mathematics
→On (A={1,2,3,4}), (aRb) if and only if the difference between (a) and (b) is divisible by (2). Choose the correct conclusion.
Class 12 · Mathematics
→If (R) is symmetric and transitive, is (R) always reflexive? Choose the correct option.
Class 12 · Mathematics
→If (R) is reflexive and transitive, which statement is always true about (R^{-1})?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(1,2),(2,1),(2,3),(3,2),(3,4),(4,3)}). Which pair must necessarily appear when making it transitive?
Class 12 · Mathematics
→On (A={1,2,3}), what is the smallest symmetric extension of (R={(1,2),(2,1),(2,3)})?
Class 12 · Mathematics
→On (A={1,2,3,4}), what is the transitive closure of (R={(1,2),(2,3),(3,4)})?
Class 12 · Mathematics
→Which pair of transitive relations gives a union that is not transitive?
Class 12 · Mathematics
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