Question

Question No. 3:
Let Q be the set of all rational numbers in R. Then show that there exists a Go set G such that
OCG and m (G)=0.​

Answer 1

Answer:

Correct option is A)

Let x∈Q, then,

f(x)=x where x∈Q

So, fof(x)=f(f(x))=f(x)=x as x∈Q

∴fof(x)=x when x∈Q

Now,

Let x∈

/

Q then

f(x)=1−x

∴fof(x)=1−(1−x)=x

as 1−x∈

/

Q as x∈

/

Q

where x∈

/

Q

fof(x)={

xwherex∈Q&x∈[0,1]

xwherex∈

/

Q&x∈[0,1]

∴ the set S=[0,1]