Define an equivalence relation p on z as follows: let x, y e z ; xpy if and only if ke z s. t. x - y = 2k show how the reflexive property and symmetric property of equivalence relations hold for p on z.

Answer with Step-by-step explanation:

We are given that an equivalence relation P on Z as

Let

if and only if such that x-y=2k.

We have to show that how the reflexive property and symmetric property of an equivalence relations hold for P on Z.

We know that reflexive property

a is related to a by given relations.

If xPax then we get

Where k=0 and 0 belongs to integers.

Hence, the relation satisfied reflexive property.

Symmetric property :If a is related to b then b is related to b.

If x and y is related by the relation

where k is any integer

k belongs to integers.

Hence, relation satisfied  symmetric property.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2