Mathematics
Equivalence relation
Practice questions
On natural numbers, (aRb) if and only if (a) and (b) have the same greatest prime factor. What kind of numbers form the equivalence class of (18)?On all ordered pairs in (R^2), ((a,b)S(c,d)) if and only if (a-b=c-d). Which is the equivalence class of ((4,1))?On all points in (R^2), (P R Q) if and only if the two points have the same (x)-coordinate. What is the equivalence class of ((3,-2))?On all points in (R^2), (P R Q) if and only if the two points are at the same distance from the origin. What does the equivalence class of ((6,8)) represent?On (A={1,2,3,4,5}), (R={(1,1),(2,2),(3,3),(4,4),(5,5),(1,2),(2,1),(2,3),(3,2)}). Which minimum pairs must be added to make it an equivalence relation?If (R) is an equivalence relation on a set (A) and ([a]\subseteq[b]), what conclusion is definite?If (R) is an equivalence relation and (a\not R b), which statement about ([a]) and ([b]) is correct?If the quotient set of an equivalence relation on (A) is (A/R={{1,4},{2,3,5}}), how many ordered pairs are in (R)?On a set with (5) elements, exactly (2) equivalence classes are required. Which option gives possible class sizes?On natural numbers, (aRb) if and only if (a) and (b) have the same product of digits. Which number belongs to the equivalence class of (23)?On all real numbers, (aRb) if and only if (a-b) is irrational. Why is this not an equivalence relation?On all real numbers, (aRb) if and only if (a-b\ge 0). Why is this not an equivalence relation?On all real numbers, (aRb) if and only if (|a|<|b|). Why is this not an equivalence relation?On all triangles, (T_1RT_2) if and only if the two triangles have the same perimeter. What type of relation is this?On the set of all circles, (C_1RC_2) if and only if the two circles have the same centre. What are the equivalence classes of this relation?On all lines, (lRm) if and only if (l) and (m) intersect. Why is this not an equivalence relation?On the set of all persons, (xRy) if and only if (x) and (y) have the same height. What type of relation is this?On all students, (xRy) if and only if (x) and (y) study in the same class. What will be the equivalence classes of this relation?On (A={1,2,3,4,5,6,7,8,9}), (aRb) if and only if (a) and (b) are both multiples of (3) or both not multiples of (3). How many ordered pairs are in this relation?On (A={1,2,3,4,5,6}), (aRb) if and only if (\min(a,b)) is odd. Is this an equivalence relation?