Solution to 15.

15. Only if both the state department and the joint chiefs of staff advise military action will the President order the armed forces into action.

Doing the grouping first, we get:

Only if (both the state department and the joint chiefs of staff advise military action) (will the President order the armed forces into action).

The simple statements are

S = The State Department advises military action.

J = The joint chiefs of staff advise military action.

P = The president orders the armed forces into action.

Substituting these back in, we get:

Only if (both S and J) (P).

Because the conjunctions follows the 'only if', it must be the consequent of the conditional, and so teh other statement must be the antecedent: