Is it true or false Which Law of Motion states that objects that are at rest tend to stay at rest and objects that are in motion tend to stay in motion unless acted upon by some outside force?

Yes, in a way. You place a cup on a table and don't expect the cup to move unless you push it or you tip the table so creating a slope down which the cup must move due to gravity and with the lessening friction with the table's surface. Therefore, friction and gravity combine to ensure your cup remains in place. So, a cup on a level table top will not move unless you give it a shove, so exerting an outside force.