# Pizza and Subs - Delivery Dilemma

### The Delivery Dilemma

The local pizza joint delivered pizza and subs. Three employees were hired to deliver: John, Heather, and Luigi.

Based on the following statements:

1. If John delivered pizza, then Heather delivered subs.
2. If John delivered subs, then Luigi delivered pizza.
3. If Heather delivered pizza, then Luigi delivered subs.

Which person or persons can we be sure always delivered the same food, and what food was it?

Heather always delivered subs.

And we can figure this out by

changing the third statement to its contrapositive, which is equivalent: "If Luigi did not deliver subs, then Heather did not deliver pizza." In other words, "If Luigi delivered pizza, then Heather delivered subs."

Now the statements we have are:

(1): If John delivered pizza, then Heather delivered subs.

(2+3): If John delivered subs, then Luigi delivered pizza. If Luigi delivered Pizza, then Heather delivered subs.

Either way, Heather must deliver subs.