Exercise B

Consider the following interpretation:

• The domain comprises only Lemmy, Courtney and Eddy

• ‘$G(x)$’ is to be true of Lemmy, Courtney and Eddy.

• ‘$H(x)$’ is to be true of and only of Courtney

• ‘$M(x)$’ is to be true of and only of Lemmy and Eddy

• ‘$c$’ is to refer to Courtney

• ‘$e$’ is to refer to Eddy

Determine whether each of the following sentences is true or false in that interpretation:

1. $H(c)$

2. $H(e)$

3. $M(c)\vee M(e)$

4. $G(c)\vee\neg G(c)$

5. $M(c)\rightarrow G(c)$

6. $\exists x\,H(x)$

7. $\forall x\,H(x)$

8. $\exists x\neg M(x)$

9. $\exists x(H(x)\wedge G(x))$

10. $\exists x(M(x)\wedge G(x))$

11. $\forall x(H(x)\vee M(x))$

12. $\exists x\,H(x)\wedge\exists x\,M(x)$

13. $\forall x(H(x)\leftrightarrow\neg M(x))$

14. $\exists x\,G(x)\wedge\exists x\neg G(x)$

15. $\forall x\exists y(G(x)\wedge H(y))$