Exercise B

Using the following symbolization key:

• domain:

  cards in a standard deck

• $B(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is black

• $C(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a club

• $D(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a deuce

• $J(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a jack

• $M(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a man with an axe

• $O(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is one-eyed

• $W(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is wild

symbolize each sentence in FOL:

1. All clubs are black cards.

2. There are no wild cards.

3. There are at least two clubs.

4. There is more than one one-eyed jack.

5. There are at most two one-eyed jacks.

6. There are two black jacks.

7. There are four deuces.

8. The deuce of clubs is a black card.

9. One-eyed jacks and the man with the axe are wild.

10. If the deuce of clubs is wild, then there is exactly one wild card.

11. The man with the axe is not a jack.

12. The deuce of clubs is not the man with the axe.