Question

If all citizens are equal, and John and Mary are citizens, then

John and Mary are equal.

John is a citizen.

Mary is a citizen
If it is wrong to take someone’s property by force, and the king has forced colonists to house and feed his soldiers rent-free, then

the king has taken property by force.

the king’s actions are wrong.

the king should make soldiers pay rent.

Answer 1

I'll treat each block as an argument and say which conclusions follow from the premises, giving a short formal sketch.

1) Citizens equal example

Premises
- All citizens are equal. (∀x∀y[(Citizen(x) ∧ Citizen(y)) → Equal(x,y)])
- John is a citizen. (Citizen(John))
- Mary is a citizen. (Citizen(Mary))

Conclusion claimed
- John and Mary are equal. (Equal(John,Mary))

Validity
- Valid. From the universal premise and the two instantiations for John and Mary you get Equal(John,Mary) by universal instantiation + modus ponens. The two sentences “John is a citizen” and “Mary is a citizen” are premises here (not consequences).

2) King/colonists example

Premises (as given or needed)
- It is wrong to take someone’s property by force. (For any agent A and victim V, if A takes V’s property by force then that action is wrong.)
- The king has forced colonists to house and feed his soldiers rent-free. (a factual claim)
- (Implicit) Forcing colonists to house/feed soldiers rent-free counts as taking their property by force.

Conclusions claimed
- The king has taken property by force.
- Follows (from the factual claim + the implicit identification that this counts as taking property by force).
- The king’s actions are wrong.
- Follows (from the first moral premise together with the conclusion that the king took property by force).
- The king should make soldiers pay rent.
- Does not follow deductively from the premises as stated. That is a prescriptive/ought claim that requires an extra normative premise linking “is wrong” to the particular remedy (e.g., “If someone wrongfully takes property, they ought to compensate or restore it” or “Wrongful takers ought to make restitution in the form of rent”). Without such a bridging normative principle you cannot validly infer the specific “should make soldiers pay rent” prescription. (This is an instance of the general point that you need normative premises to derive specific ought-conclusions.)

Summary
- First argument: valid; conclusion follows.
- Second argument: the factual and moral premises suffice to infer the king took property by force and that his actions are wrong, but they do not by themselves entail the specific policy-prescription that the king should make soldiers pay rent — you need an extra normative premise to reach that.