Solution to 14.

14. If it is necessary for one to get a car loan that one have good credit, then it is sufficient for one to have good credit that one get a car loan.

Doing the groupings, we have

If (it is necessary for one to get a car loan that one have good credit), then (it is sufficient for one to have good credit that one get a car loan).

Clearly the entire statement is a conditional. The simple statements are:

L = One gets a car loan.

C = One has good credit.

Substitutung we have:

If (it is necessary for L that C), then (it is sufficient for C that L)

The antecedent involves a necessary condition, and so it too will be a conditional. The necessary condition is the consequent, and in this case the necessary condition is C, and what it is neccessary for is L. So we get

If (if L then C), then (it is sufficient for C that L)

The antecedent involves sufficient conditions, and so it too is a conditional. The sufficient condition is always the antecedent of the conditional,and what it is sufficient for is the consequent. Clearly, the sufficient condition is L, and what it is sufficient for is C:

If (if L then C), then (if L then C)

So we have