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Class 11 · Mathematics
→If (R) and (S) are both equivalence relations on (A), which statement about (R\cap S) is always true?
Class 11 · Mathematics
→On (A={1,2,3,4,5}), (R={(a,b):a+b\leq6}). Choose the correct option about (R).
Class 11 · Mathematics
→On (\mathbb{R}), (aRb) if and only if (a-b) is rational. How are the equivalence classes of (R) formed?
Class 11 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) have the same greatest prime factor. What kind of relation is it?
Class 11 · Mathematics
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}). Is (R) antisymmetric?
Class 11 · Mathematics
→On (A={1,2,3}), (R={(1,2),(2,3)}). Which pairs will be added in the symmetric closure?
Class 11 · Mathematics
→On (A={1,2,3}), (R={(1,2),(2,1)}). Which pairs will be added in the reflexive closure?
Class 11 · Mathematics
→On (A={1,2,3,4}), (R={(1,2),(2,3),(3,4)}). What is the minimum number of new pairs needed in the transitive closure of (R)?
Class 11 · Mathematics
→Which pair is compulsory in the transitive closure of a relation (R), if (R) contains ((1,2)) and ((2,4))?
Class 11 · Mathematics
→On (A={1,2,3}), relation (R={(1,1),(1,2),(2,2),(2,3),(1,3),(3,3)}) is given. Which familiar order does this relation resemble?
Class 11 · Mathematics
→On (A={1,2,3,4}), (aRb) if and only if (a\neq b). Which statement about (R) is correct?
Class 11 · Mathematics
→On (\mathbb{N}), (aRb) if and only if (a+b) is odd. What is the correct statement about (R)?
Class 11 · Mathematics
→On (\mathbb{R}), (aRb) if and only if (a^3\leq b^3). This relation is equivalent to which relation?
Class 11 · Mathematics
→On (\mathbb{R}), (aRb) if and only if (a-b>0). Which property of (R) is correct?
Class 11 · Mathematics
→On (A={1,2,3,4,5}), (R={(a,b):|a-b|\leq1}). Which statement about (R) is correct?
Class 11 · Mathematics
→On (A={1,2,3,4}), (R={(a,b):a-b) is divisible by (3)(}). How many ordered pairs are in (R)?
Class 11 · Mathematics
→If (R) is symmetric, what is its relation with (R^{-1})?
Class 11 · Mathematics
→If (R) is a reflexive relation on (A), which statement about (R^{-1}) is correct?
Class 11 · Mathematics
→On (A={1,2,3}), the identity relation is (I_A={(1,1),(2,2),(3,3)}). What is the correct nature of (I_A)?
Class 11 · Mathematics
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