Hi,

So... I've decided to study some algebra, to see if I can handle it... lol

I've come accross this (very basic) question, which may rather be set theory, but the original question is algebra :

Let G be a group. Let H be a subgroup containing a subset P.

Prove that

So basically, I have to prove that

Where and

It is clear that

So it is very logical to have the equality

But I didn't succeed in finding a formal proof

Thanks,