1 Which of the following can be validly inferred from Bb Ba

1- Which of the following can be validly inferred from Bb • ~Ba by Existential Generalization?

a) ($y)By • ~Ba
b) ($x)Bb • ~Bx
c) ($x)(Bb • ~Bx)
d) $x)~Bx

2- Which of the following is an instance of (x)[Lx ($y)(Ly Gyx)]?

a) La ($y)(Ly Gyx)
b) La ($y)(Ly Gyb)
c) La ($y)(Ly Gya)
d) Lx ($y)(Ly Gyz)

3- In which of the following is the variable \"x\" free?

a) ($x)Fx • Gy
b) ($x)(y)(Gy Fx)
c) (x)((Fx • Gx) Hx)
d) Fx • (x)(Gx Hx)

4- All of the following are well-formed formulas of predicate logic except

a) (a)Fa.
b) (w)Pw.
c) ($y)($x)(Ly Mx).
d) Hx Bd.

5- In logicese, (x)~Fx says

a) everything is an F.
b) nothing is an F.
c) something is an F.
d) there is at least one F.

Solution

1- Which of the following can be validly inferred from Bb • ~Ba by Existential Generalization?

a) ($y)By • ~Ba
b) ($x)Bb • ~Bx
c) ($x)(Bb • ~Bx)
d) $x)~Bx

d) is the correct option.

2- Which of the following is an instance of (x)[Lx ? ($y)(Ly ? Gyx)]?

a) La ? ($y)(Ly ? Gyx)
b) La ? ($y)(Ly ? Gyb)
c) La ? ($y)(Ly ? Gya)
d) Lx ? ($y)(Ly ? Gyz)

(b) is the correct option.

3- In which of the following is the variable \"x\" free?

a) ($x)Fx • Gy
b) ($x)(y)(Gy ? Fx)
c) (x)((Fx • Gx) ? Hx)
d) Fx • (x)(Gx ? Hx)

(c) is the correct option.

4- All of the following are well-formed formulas of predicate logic except

a) (a)Fa.
b) (w)Pw.
c) ($y)($x)(Ly ? Mx).
d) Hx ? Bd.

(a)Fa is not the well formeed formula of predicate logic.Therefore, (a) is the correct option.

5- In logicese, (x)~Fx says

a) everything is an F.
b) nothing is an F.
c) something is an F.
d) there is at least one F.

(b) is the correct answer.