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Class 12 · Mathematics · Hard
→On (A={1,2,3,4,5,6}), (aRb) iff (a) and (b) leave the same remainder on division by (3). What is the class of (2)?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R={(a,b): |a-b|) is even(}). How many equivalence classes are formed?
Class 12 · Mathematics · Hard
→If a relation always contains ((a,c)) whenever it contains ((a,b)) and ((b,c)), which property does it have?
Class 12 · Mathematics · Hard
→On (A={1,2,3}), (R={(1,1),(2,2),(1,2),(2,3),(1,3)}). Which property does this relation satisfy?
Class 12 · Mathematics · Hard
→If (A) has (n) elements, which formula gives the total number of relations on (A)?
Class 12 · Mathematics · Hard
→On (A={1,2,3}), (R={(1,2),(2,1),(2,3),(3,2)}). Which property does this relation satisfy?
Class 12 · Mathematics · Hard
→On real numbers, (aRb) iff (a<b). Which statement is correct?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R={(a,b):a+b) is even(}). What type of relation is it?
Class 12 · Mathematics · Hard
→On integers, (aRb) iff (a) and (b) leave the same remainder when divided by (4). What is the equivalence class of (0)?
Class 12 · Mathematics · Hard
→If (R) is an equivalence relation on (A), which statement about its equivalence classes is correct?
Class 12 · Mathematics · Hard
→Which statement is always true for the universal relation on a set (A)?
Class 12 · Mathematics · Hard
→Which is the smallest reflexive relation on (A={1,2,3})?
Class 12 · Mathematics · Hard
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1)}). What type of relation is it?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), relation (R={(a,b):a) divides (b)(}). What type of relation is it?
Class 12 · Mathematics · Hard
→How many relations on (A={1,2,3}) are both reflexive and symmetric?
Class 12 · Mathematics · Hard
→How many symmetric relations are there on (A={1,2,3})?
Class 12 · Mathematics · Hard
→If (A) has (4) elements, what is the number of reflexive relations on (A)?
Class 12 · Mathematics · Hard
→If (A={1,2,3}), how many total relations can be formed from (A) to (A)?
Class 12 · Mathematics · Medium
→Let A={1,2,3}. If a symmetric relation R on A must contain (1,2), how many such relations are possible?
Class 12 · Mathematics · Medium
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