Exercise A

Consider the following interpretation:

• The domain comprises only Corwin and Benedict

• ‘$A(x)$’ is to be true of both Corwin and Benedict

• ‘$B(x)$’ is to be true of Benedict only

• ‘$N(x)$’ is to be true of no one

• ‘$c$’ is to refer to Corwin

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

1. $B(c)$

2. $A(c)\leftrightarrow\neg N(c)$

3. $N(c)\rightarrow(A(c)\vee B(c))$

4. $\forall x\,A(x)$

5. $\forall x\neg B(x)$

6. $\exists x(A(x)\wedge B(x))$

7. $\exists x(A(x)\rightarrow N(x))$

8. $\forall x(N(x)\vee\neg N(x))$

9. $\exists x\,B(x)\rightarrow\forall x\,A(x)$