Intersection of two subgroups: Why is it necessarilly true that intersection is a subgroup?

[Boi]

So, I've decided to try to learn some Group Theory (don't ask why) and I kept bumping in this thing: usually, whenever people talk about two subgroups (for example $K$ and $H$) of some subgroup $G$ they immediately say that $K \cap H$ is necessarily a subgorup of both $K$ and $H$. Could you explain why is this necessarily true, please? Or at least give me a hint?

 

[Boi]

Nevermind, I'd figured it out (god, now I feel dumb).

 

[khansaheb]

So, I've decided to try to learn some Group Theory (don't ask why) and I kept bumping in this thing: usually, whenever people talk about two subgroups (for example $K$ and $H$) of some subgroup $G$ they immediately say that $K \cap H$ is necessarily a subgorup of both $K$ and $H$. Could you explain why is this necessarily true, please? Or at least give me a hint?

Have you learnt about Venn diagram?

 

[pka]

Have you learnt about Venn diagram?

I am curious as to know what Venn diagrams have to do with the intersection of subgroups of a group?

 

[khansaheb]

Through Venn diagram it can be graphically represented that

two subgroups (for example K and H ) of some subgroup G they immediately say that K∩H is necessarily a subgorup of both K and H

And of course you want it to be proven symbolically

 

[Steven G]

Have you learnt about Venn diagram?

Can we see an example how you can prove this using venn diagrams?

 

[khansaheb]

Really!!

I politely refuse to enter into this bantering!!!