Should it be necessary to have a PS2, PS3 AND PS4 hooked up all at once to play?

[Farsala]

Should have gotten a BC PS3 if one valued it so much. Optimal for me PS3, to play PS1,PS2,PS3 games. I will not buy PS4 until I know a price. And I am used to having multiple consoles hooked up to the same tv. Last gen I had xbox,gamecube and PS2. Same thing for this gen and Will probably be the same next gen.