Yes. However, this is very dependent upon the context. You get 1 Normal Summon OR Set per turn. A Set is usually the placing of a monster from your hand into an available Monster Card Zone, both face-down and horizontally - or put more simply "face-down Defense Position." A "1 Normal Summon or Set" Set does NOT count as a Summon, so the opponent cannot activate Trap Hole in response to a Set.

To Normal Summon or Set a Level 5 or higher monster, you must Tribute the respective number of monsters (exactly 1 for 5-6, exactly 2 for 7+). You still have to Tribute monsters to Set a Level 5 or higher monster, and this counts for your "1 Normal Summon or Set", it is treated as a Set.

That said, there are other "special" Set situations that do not count for the "1 Normal Summon or Set per turn" rule. Flipping a monster face-down with a card effect. This includes the monster's own effect (such as Stealth Bird or Guardian Sphinx), and well as other cards' effects like Book of Moon or Darkness Approaches. Darkness Approaches is especially interesting because a monster can be "Set" in Attack Position in this way.

Generally, if a monster is Special Summoned in face-down Defense Position (as with Spear Cretin, A Shallow Grave, or Cyber Jar), this counts as a Set as well as a Special Summon. In a situation like this, your opponent can activate cards triggered by either the Set (such as the TCG effect for Shadow of Eyes) or the Special Summon. For example, a "1 Normal Summon or Set" Set cannot trigger Torrential Tribute, but if it was Set by Cyber Jar, then Torrential Tribute CAN be activated.

The card Light of Intervention changes things up a bit. When Light of Intervention is active, card effects that flip a monster face-down cannot be activated. But card effects that Special Summon a monster in face-down Defense Position (this would count as a Set) Special Summon it in face-up Defense Position instead, and it is not counted as a Set. If you try to "1 Normal Summon or Set" Set a monster while Light of Intervention is on the field, then it is Normal Summoned in face-up Defense Position, and it is not counted as a Set.

In show (Ni-Ki-Oh!) rules, a monster can be Normal Summoned in face-up Defense Position if the player does not wish it face-down. This is not considered a Set.