Question

Create a partition of our class. It must be made of at least 3 subsets, and fewer than total number of people in the class. (So you cannot have the partition be each separate person in their own subset.) List the subsets of your partition. Explain the equivalence relation that matches your partition.

Answer 1

Solni And K be an Let the class has n students. Teen integer such that 3<k cn. So, if we list the soll no. of all the students, partition them in in 'k' sets [] = {x: 2 = 0 {mad *)) [ ] = { x = 1 (madk); then, we can nink-1 f any arbitrary ay Ex. Then [K-1] = &n: 2 = (modk) where x i the roll no. students The equivalence relation that neath matches this partition is- let, x be the set of Ich soll. no. of all students and a R(x, y) & in 't divides anyl This relation is equivalence As, Bole ao fogoro k divides (ara) So, R(a ,a) k divides carb) then (b-a)=-(arb) k divide (bra). So, R(a, b) = R(b, a ta, bex k divides farb) and K divides (b.c) earc) = (a - b) + (6-6), so, k dincks fare) Thus, R(a,b) and R(b, c) R(a, () & a, b, c ex наех, st then,