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Class 11 · Mathematics
→On the set \(A=\{1,2,3,\ldots,15\}\), a relation \(R\) is defined by \(aRb\) if and only if \(a\equiv b\pmod{6}\). Which of the following is the equivalence class \([8]\) in \(A\)?
Class 11 · Mathematics
→On the real numbers, define aRb if and only if a^3 = b^3. What type of relation is R?
Class 11 · Mathematics
→On real numbers, (aRb) if and only if (a+b=0). What type of relation is it?
Class 11 · Mathematics
→On the set of real numbers, a relation R is defined by aRb if and only if \(|a-b|\leq 2\). Choose the correct statement.
Class 11 · Mathematics
→On (A=\mathbb{R}\setminus{0}), (aRb) if and only if (ab>0). What are its equivalence classes?
Class 11 · Mathematics
→On non-zero integers, (aRb) if and only if (\frac{a}{b}>0). What type of relation is it?
Class 11 · Mathematics
→On positive integers, (aRb) if and only if (a\mid b) and (b\mid a). Which relation is this?
Class 11 · Mathematics
→On the set \(A=\{-2,-1,0,1,2,3\}\), define the relation \(R\) by \(aRb\) if and only if \(a\equiv b\pmod{3}\). What is the equivalence class \([-1]\)?
Class 11 · Mathematics
→On the set \(A=\{0,1,2,3,4,5,6,7\}\), define a relation \(R\) by \(aRb\) if and only if \(a^2\equiv b^2\pmod{8}\). What is the equivalence class \([1]_R\) of 1 under \(R\)?
Class 11 · Mathematics
→How many equivalence relations on a (4)-element set have exactly (2) equivalence classes?
Class 11 · Mathematics
→What is the total number of equivalence relations on a set with (3) elements?
Class 11 · Mathematics
→How many ordered pairs are in the equivalence relation induced by the partition \(P=\{\{1,4\},\{2,3,5\}\}\) of the set \(\{1,2,3,4,5\}\)?
Class 11 · Mathematics
→The set (A) is partitioned into classes (P={{1,2},{3,4,5},{6}}). How many ordered pairs are in the equivalence relation formed by it?
Class 11 · Mathematics
→On (A={1,2,3,4}), (R={(1,2),(2,3),(3,4)}). Which extra pairs will be in the transitive closure?
Class 11 · Mathematics
→On (A={1,2,3,4,5}), (R={(1,2),(2,4),(4,5)}). What is the minimum number of pairs to add to make (R) transitive?
Class 11 · Mathematics
→For (A={1,2,3}), the matrix of relation is (M_R=\begin{pmatrix}1&1&0\0&1&1\0&0&1\end{pmatrix}). Choose the correct statement.
Class 11 · Mathematics
→For (A={1,2,3}), the matrix of relation is (M_R=\begin{pmatrix}1&0&1\0&1&0\1&0&1\end{pmatrix}). What type of relation is (R)?
Class 11 · Mathematics
→On students of a class, (aRb) if and only if (a) and (b) have the same birth month. What type of relation is it?
Class 11 · Mathematics
→On the set of triangles, (T_1RT_2) if and only if (T_1) and (T_2) are similar. What type of relation is it?
Class 11 · Mathematics
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