Use your propositional logic tools, including inferences to solve this puzzle. The grid is provided for you to keep track of conclusions as you arrive at them.Don't forget about negations, inferences, etc.

Key:Some columns have abbreviations:

Pizza: C = Cheese

P = Pepperoni

S = Sausage

D = Deluxe

Plate Color:

W = White

B = Blue

R = Red

Y = Yellow

For the sake of this exercise, it is assumed that Charles and Paul and male, and Sue and Diane are female.

Use the following statements to determine which person ate which pizza, on which colour plate, and what they paid for their pizza.

1:No more than 1 woman and 1 man ordered a pizza type that started with the same letter as their first name. No fewer than 1 woman and 1 man ordered a pizza type that started with the same letter as their first name.

2: A man at pizza from a blue plate. A woman ate pizza from a red plate.

3: A woman ordered the $15 pizza.

4:Charles and Sue didn't eat pizza from a yellow plate.

5:The person who ordered the pepperoni pizza paid $2 less than Diana.

6:The person who ate pizza from the white plate didn't order the deluxe pizza.

7:The person who ate the pizza from the blue plate didn't order the pepperoni pizza.

8:Paul ate pizza from the white plate or ordered the sausage pizza.

9:The cheese pizza costs more than the deluxe pizza.

10:Charles ordered the sausage pizza or paid $11 for his pizza.

11:The person who ordered the sausage pizza didn't pay $13.

12:The people who ate pizza from the white and blue plates paid $28 total for their pizzas.

13:Paul did not pay $17 for his pizza.

Pizza Cost C P D W 11 13 15 17 Charles Paul Name Sue Diana 11 13 Cost 15 17 White Blue Plate Red Yellow