(10 pts) a relation r is defined on the set z by "a r b if a - b is divisible by 5" for a, b e z. examine if r is an equivalence relation on z.

Yes

Step-by-step explanation:

Given that a relation R is defined on the set Z by "a R b if a - b is divisible by 5

for a, b in the set of integers.

Reflexive:

We have

for any a,

i.e. (a,a) is related. Hence reflexive

ii) Symmetric:

If a-b is divisible by 5, then b-a is also divisible by 5.  Hence symmetric

iii) Transitive

If

adding we get

Hence R is transitive

It follows that R is an equivalence relation on Z

the median here is 25. your lowest value is 14 and highest value is 48. to find the third quartile, find the medium number in between 25 and 48 which would be 42 i believe.

it depends on the weather. because i have flown to seattle when it was pouring down rain and there was one time i flew to ohio when it was snowing hard. whats your situation.

step-by-step explanation: