Mathematics
Equivalence relation
Practice questions
On (A={1,2,3,4,5,6}), (aRb) holds when (\max(a,4)=\max(b,4)). Which is the equivalence class of (2)?On (A={1,2,3,4,5,6}), how many equivalence classes are formed by the relation (\max(a,4)=\max(b,4))?For points in the plane, (P R Q) holds when (P) and (Q) have the same distance from the origin. Which point belongs to the equivalence class of ((3,4))?For points in the plane, what kind of equivalence classes are formed by the relation of having the same distance from the origin?If (R) and (S) are equivalence relations on (A) and (R\subseteq S), what is the relation between the classes of (R) and the classes of (S)?On (A={1,2,3,4,5,6}), (R) has classes ({1,2},{3,4},{5,6}), and (S) has classes ({1,2,3,4},{5,6}). Which statement is correct?On (A={1,2,3,4}), (R) has classes ({1,2},{3,4}), and (S) has classes ({1,3},{2,4}). What are the classes of (R\cap S)?On real numbers, (aRb) holds when (a-b\in\mathbb{Q}). Which element belongs to the class of (\sqrt{2}+\sqrt{3})?On non-zero real numbers, (aRb) holds when (\frac{a}{b}) is a positive rational number. Which element is in the class of (-2\sqrt{5})?On integers, (aRb) holds when (a^3\equiv b^3 \pmod{7}). Why is this an equivalence relation?On (A={1,2,3,4,5,6,7,8}), (aRb) holds when (a^2\equiv b^2 \pmod{5}). Which is the equivalence class of (2)?On (A={1,2,3,4,5,6,7,8}), how many equivalence classes are formed by (a^2\equiv b^2 \pmod{5})?On the set of all subsets of (S={1,2,3,4,5}), (A R B) holds when (|A|=|B|). How many members are in the equivalence class of a (3)-element subset?On the set of all subsets of (S={1,2,3,4}), (A R B) holds when (|A\cap{1,2}|=|B\cap{1,2}|). What is the size of the equivalence class of ({1,3})?On (A={1,2,3,4,5}), relation (R) contains all diagonal pairs and ((1,2),(2,1),(2,4),(4,2)). Which minimum pairs must be added to make it an equivalence relation?On (A={1,2,3,4}), let (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,4),(4,3)}). Which statement about (R) is correct?If (R) is an equivalence relation on (A) and ([a]) has exactly (4) elements, how many ordered pairs of (R) come from inside ([a])?If (R) is an equivalence relation and (a\in[b]), (b\in[c]), which conclusion is correct?On (A={1,2,3,4,5,6,7,8}), (aRb) holds when (a) and (b) have the same status of being a multiple of (2) and the same status of being a multiple of (4). Which is the equivalence class of (6)?On integers, (aRb) holds when (a\equiv b \pmod{3}), and (aSb) holds when (a\equiv b \pmod{5}). In (R\cap S), which is the equivalence class of (7)?