Mathematics
Equivalence relation
Practice questions
On integers, (aRb) holds when (a-b) is divisible by (7). Which is the equivalence class of (15)?On (A={1,2,3,4,5,6,7}), (aRb) holds when (a) and (b) have the same remainder on division by (3). Which is the equivalence class of (4)?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,4),(4,1)}) is given. What are its equivalence classes?If an equivalence relation has classes ({p,q,r}) and ({s}), how many ordered pairs are in the relation?On integers, (aRb) holds when (a\equiv b \pmod{8}). How many distinct equivalence classes are there?On real numbers, (aRb) holds when (a^3=b^3). What type of relation is it?On (A={-2,-1,0,1,2}), (aRb) holds when (a^2=b^2). Which is the equivalence class of (1)?On (A={1,2,3,4,5}), (aRb) holds when (|a-b|) is divisible by (3). Which pair belongs to (R)?If (R) is an equivalence relation and (aRb) is false, which statement about ([a]) and ([b]) is correct?Which option gives a valid partition of (A={1,2,3,4,5})?On (A={1,2,3}), why is (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}) not an equivalence relation?On real numbers, (aRb) holds when (a-b) is an integer. What type of relation is it?For the relation on real numbers where (a-b) is an integer, which element is in the same class as (\frac{1}{2})?On (A={1,2,3,4,5,6}), (aRb) holds when (a+b) is divisible by (2). Which is the equivalence class of (2)?If (R) is an equivalence relation on a set (A), what does ({[a]:a\in A}) represent?For the partition ({1,2,4},{3}) of (A={1,2,3,4}), which pair will not be in the corresponding equivalence relation?Which option can be the classes of an equivalence relation on (A={1,2,3,4})?On (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) are both multiples of (3) or both not multiples of (3). What type of relation is it?In the relation on (A={1,2,3,4,5,6}) based on being multiples of (3) or not multiples of (3), what is the equivalence class of (5)?If a relation always has ((b,a)\in R) whenever ((a,b)\in R), which property is this?