Solution to 12.

12. I will buy a new car and a new suit only if neither my bank account is empty nor my stocks have lost value.

We have a compound predicate in the first part of this statement. Expanding it out we get:

I will buy a new car and I will buy a new suit only if neither my bank account is empty nor my stocks have lost value.

The simple statements are:

C = I will buy a new car.

S = I will buy a new suit.

B = My bank account is empty.

L = My stocks have lost value.

Substituting we get:

C and S only if neither B nor L

The grouping is clearly:

(C and S) only if (neither B nor L)

It could also be grouped as:

C and {S only if (neither B nor L)}

This grouping isn't wrong, since the original statement is logically ambiguous in this way. But given the meaning of the expressions, it seems most likely that the first is the correct grouping:

(C and S) only if (neither B nor L)

Recall that with an 'only if' the statement following the 'if' is the consequent. And this time we can translate the 'neither nor' as a conjunction of negations. So we have: