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When an ability states to “add 1 to saving throws to this unit” such as the AM stratagem “Take Cover!” Can that be applied to either an armor save or if the unit has one, an invulnerable save?

From the Main Rulebook FAQ:

Q: If an ability allows me to add 1 to saving throws, does it apply to both normal saving throws and invulnerable throws?

A: Yes, unless otherwise stated. Remember that invulnerable saves are unaffected by the +1 bonus models receive to their saving throws for the benefits of cover.

 The Philosopher wrote:
When an ability states to “add 1 to saving throws to this unit” such as the AM stratagem “Take Cover!” Can that be applied to either an armor save or if the unit has one, an invulnerable save?

There is no such thing as an "armour" save in 40k, there is only Save and Invulnerable save.

If a rule says save, it applies to both Saves and Invulnerable Saves, as Ghaz quoted.

However, Take Cover! received errata to only apply to "Armour Saves", whatever those are. As such it is no longer functional in any practical sense, while still theoretically being a thing you can do.

Disclaimer: This is a strictly RaW answer, I cannot speak for the intentions of the rules writers, how others interpret or define certain colloquial phrases, nor how others may choose to interpret the errata to Codex: Astra Copywritum for the 8th edition of Warhammer 40,000, published by Games Workshop PLC.

 BaconCatBug wrote:
There is no such thing as an "armour" save in 40k...

This statement is of course false.

Armor save is detailed on P. 13 of the 40k Battle Primer.

Save (Sv): This indicates the protection a model’s armour gives.

And of course weapons have a thing called Armour Penetration...

Armour Penetration (AP): How good it is at getting through armour.

Therefore what you call a save, is actually an armor save.

the 40k book just says save because it is shorted, but clearly it is detailed as protection in the form of "armour" so it is absolutely an armour save.

 DeathReaper wrote:
the 40k book just says save because it is shorted, but clearly it is detailed as protection in the form of "armour" so it is absolutely an armour save.

By that logic, a Heavy Plasma Cannon is the same as a Plasma Cannon. Just because the additional fluff blurb states it represents a models armour, doesn't change the name of the characteristic, which is Save, not Armour Save.

Anyway, I've said my piece, this will be the last I will speak of it.

 BaconCatBug wrote:

 DeathReaper wrote:
the 40k book just says save because it is shorted, but clearly it is detailed as protection in the form of "armour" so it is absolutely an armour save.

By that logic, a Heavy Plasma Cannon is the same as a Plasma Cannon.

That is not the same situation at all. Strawman arguments like that do not help.

Just because the additional fluff blurb states it represents a models armour, doesn't change the name of the characteristic, which is Save, not Armour Save.

it is not fluff, it is extra information about the save and Armour Penetration...

please ignore BCB on this issue their are multiple threads on it where everyone ignores him. A RAW way of doing things doesnt apply when the RAW doesn't work because armour save don't exist in 40k. Therefore we default to RAI and everyone knows what they mean by armour save.

and by +1 to armour save they mean the saving throw and not the invul for take cover (useng the faq'd changed text).

While the AM psychic power adds one to the saving throws it means both saving throw and invulnerable saves