How to approach your boyfriend

How do you know they are lies?

They are lies cause I see him with the person's and he denies it with no remorse at all

You can sit down with him and ask him why he feels the need to be dishonest about the situation. Give him the opportunity to explain.
Now my question to you is--Why would you want to stay in a relationship with someone whom will lie directly to your face?

When you catch them in a lie, and they keep lying, you leave and disappear from their life.

Talking to a liar and expecting the truth is insane.