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Class 12 · Mathematics
→On (A={1,2,3,4}), what are the equivalence classes of the identity relation (I={(1,1),(2,2),(3,3),(4,4)})?
Class 12 · Mathematics
→For (A={1,2,3,4}), let (R=A\times A). How many equivalence classes does this relation have?
Class 12 · Mathematics
→Which option states a general property of classes formed by an equivalence relation?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) holds when (a\equiv b \pmod{2}). Which partition is formed by this relation?
Class 12 · Mathematics
→If (R) is an equivalence relation, why can ([a]) not be empty?
Class 12 · Mathematics
→If (R) is an equivalence relation and ([a]=A), which statement about (a) is correct?
Class 12 · Mathematics
→If (A) has (5) elements and the sizes of the equivalence classes are (2,2,1), how many pairs are in the relation?
Class 12 · Mathematics
→On (A={1,2,3,4}), (aRb) holds when (a=b) or ({a,b}={1,2}). What are the classes of this relation?
Class 12 · Mathematics
→Which option gives a transitive relation on (A={1,2,3})?
Class 12 · Mathematics
→Which option gives a symmetric relation on (A={1,2,3})?
Class 12 · Mathematics
→Which option gives a reflexive relation on (A={1,2,3})?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), what are the equivalence classes of (R={(1,1),(2,2),(3,3),(4,4),(5,5),(1,5),(5,1),(2,4),(4,2)})?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) are both less than (4) or both not less than (4). What is the equivalence class of (2)?
Class 12 · Mathematics
→For lines in a plane, (lRm) holds when (l) and (m) are parallel or identical. What type of relation is it?
Class 12 · Mathematics
→For the relation on natural numbers based on having the same number of digits, which is the equivalence class of (145)?
Class 12 · Mathematics
→On natural numbers, (aRb) holds when (a) and (b) have the same number of digits. What type of relation is it?
Class 12 · Mathematics
→Which relation is transitive but generally not symmetric?
Class 12 · Mathematics
→If (R) is an equivalence relation and ((x,y)\in R), which statement must be true?
Class 12 · Mathematics
→If ([a]={2,5,8}) and the relation is an equivalence relation, which pair must surely belong to the relation?
Class 12 · Mathematics
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