(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

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

you can use a^2+ b^2=c^2