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Class 12 · Mathematics
→How many equivalence relations on (A={1,2,3,4,5}) have (1) alone in its own class?
Class 12 · Mathematics
→If (A) has (5) elements, how many equivalence relations are possible on (A)?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6,7,8,9}), (aRb) holds when the digit sums of (a) and (b) give the same remainder modulo (3). Which is the equivalence class of (8)?
Class 12 · Mathematics
→On real numbers, (aRb) holds when (|a-1|=|b-1|). Which is the equivalence class of (-2)?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6,7,8}), (aRb) holds when (a) and (b) have the same status of divisibility by (3) and by (4). Which is the equivalence class of (8)?
Class 12 · Mathematics
→If (R) is an equivalence relation and ([a]\subseteq [b]\cup[c]), with ([a]\cap[b]\neq\varnothing), which conclusion is correct?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6,7,8,9,10}), how many equivalence classes are formed by the relation (\tau(a)=\tau(b))?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6,7,8,9,10}), (aRb) holds when (\tau(a)=\tau(b)), where (\tau(n)) is the number of positive divisors. Which is the equivalence class of (6)?
Class 12 · Mathematics
→On real numbers, (aRb) holds when (\cos a=\cos b). Which is the correct form of the equivalence class of (0)?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), for the relation where (a+b) is divisible by (7) or (a=b), how many ordered pairs are there?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) holds when (a+b) is divisible by (7) or (a=b). What are the classes of this relation?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), relation (R) contains all diagonal pairs, ((1,2),(2,1),(2,5),(5,2)). Which minimum pairs must be added to make it an equivalence relation?
Class 12 · Mathematics
→On integers, (aRb) holds when (a\equiv b \pmod{4}), and (aSb) holds when (a\equiv b \pmod{6}). In (R\cap S), what is the equivalence class of (14)?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (R) has classes ({1,2,3},{4,5,6}), and (S) has classes ({1,4},{2,5},{3,6}). How many classes are in (R\cap S)?
Class 12 · Mathematics
→If (R) and (S) are equivalence relations on (A), the classes of (R\cap S) are obtained from what?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6,7,8}), (aRb) holds when (a) and (b) have the same divisibility status by (4) and by (2). How many equivalence classes are formed?
Class 12 · Mathematics
→On the set of all subsets of (S={1,2,3,4,5,6}), (A R B) holds when (|A|=|B|). How many members are in the equivalence class of a (2)-element subset?
Class 12 · Mathematics
→On integers, (aRb) holds when (a-b) is divisible by (8) or by (12). Why is this relation not an equivalence relation?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) have the same remainders modulo (2) and modulo (5). Which is the equivalence class of (3)?
Class 12 · Mathematics
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