Monadic Paradigms

Question 1

(∀x)(Fx ⊃ Gx)

Answer 1

a. All F’s are G’s

b. The extension of F is a subset of the extension of G.

Question 2

(∃x)(Fx . Gx)

Answer 2

a. Some F’s are G’s

b. The intersection of the extensions of F and G is non-empty.

Question 3

(∀x)(Fx . Gx)

Answer 3

a. Everything is both an F and a G

b. Everything in the universe of discourse is in the intersection of the extensions of F and G.

Question 4

(∀x)(Fx v Gx)

Answer 4

a. Everything is either an F or a G

b. Everything in the universe of discourse is in the union of the extensions of F and G.

Question 5

(∃x)(Fx v Gx)

Answer 5

a. Something is either an F or a G

b. The union of the extensions of F and G is non-empty.

Question 6

(∀x)(Fx ≡ Gx)

Answer 6

a. All and only F’s are G’s

b. The extension of F is the extension of G.

Question 7

-(∃x)(Fx . Gx)

Answer 7

a. No F is G

b. The extensions of F and G are disjoint.

Question 8

(∃x)(Fx . -Gx)

Answer 8

a. Some F is not G

b. There is something which is a member of the extension of F but not G.

Question 9

(∀x)(Fx ⊃ -Gx)

Answer 9

a. No F is G

b. The extensions of F and G are disjoint.

Question 10

(∃x)(Fx ≡ Gx)

Answer 10

b. At least one member in the universe of discourse is either in the extensions of both F and G or not in the extensions of F or G.

Question 11

(∃x)(Fx ⊃ Gx)

Answer 11

b. At least one member in the universe of discourse is either not in the extension of F or not in the extension of G.