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Return to Introduction to Formal Logic Student Resources
Section 5.07 Self-Quiz
Quiz Content
*
not completed
.
Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∀x)(Ax ⊃ Bx)
2. Aa
3. a=f(b)
Af(a) ⊃ Ba
correct
incorrect
Aa ⊃ Bf(a)
correct
incorrect
Aa ⊃ Bf(b)
correct
incorrect
Af(b)
correct
incorrect
Ab
correct
incorrect
*
not completed
.
Which of the following propositions is derivable from the given premises in F?
1. (∀x)(Ax ⊃ Bx)
2. Aa
3. a=f(b)
(∃x)Bf(x)
correct
incorrect
(∀x)Ax
correct
incorrect
(∀x)Bf(x)
correct
incorrect
b=f(a)
correct
incorrect
Af(a)
correct
incorrect
*
not completed
.
Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∀x)[Dx ⊃ Df(x)]
2. (∀x)[Ex ⊃ (Dx ≡ ~Fx)]
3. Ea • ~Fa
Ea ⊃ [Df(a) ≡ ~Ff(a)]
correct
incorrect
Ea ⊃ [Df(a) ≡ ~Fa]
correct
incorrect
Da ⊃ Da
correct
incorrect
Df(a) ⊃ Df(a)
correct
incorrect
Df(a) ⊃ Df(f(a))
correct
incorrect
*
not completed
.
Which of the following propositions is derivable from the given premises in F?
1. (∀x)[Dx ⊃ Df(x)]
2. (∀x)[Ex ⊃ (Dx ≡ ~Fx)]
3. Ea • ~Fa
Df(f(a))
correct
incorrect
Ef(a)
correct
incorrect
Ef(f(a))
correct
incorrect
(∀x)Df(f(x))
correct
incorrect
Df(a)Ff(a)
correct
incorrect
*
not completed
.
Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∀x)(∀y)f(x,y)=g(y,x)
2. e=f(a,b)
3. e=g(a,b)
(∀y)f(x,y)=g(y,a)
correct
incorrect
(∀y)f(a,y)=g(a,y)
correct
incorrect
(∀y)f(a,y)=g(y,a)
correct
incorrect
(∀y)f(g(a,b),y)=g(a,b)
correct
incorrect
(∀y)f(g(a,b),y)=g(b,g(b,a))
correct
incorrect
*
not completed
.
Which of the following propositions is derivable from the given premises in F?
1. (∀x)(∀y)f(x,y)=g(y,x)
2. e=f(a,b)
3. e=g(a,b)
(∀x)(∀y)f(x,y)=f(y,x)
correct
incorrect
(∀x)(∀y)g(x,y)=g(y,x)
correct
incorrect
(∃x)(∃y)g(x,y)=g(y,x)
correct
incorrect
(∃x)f(x,f)=g(a,b)
correct
incorrect
f(b,a)≠f(a,b)
correct
incorrect
*
not completed
.
Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∀x)(∀y)[f(x)=f(y) ≡ x=y]
2. Ja • ~Jb
(∀y)[x=y ≡ x=y]
correct
incorrect
(∀y)[a=f(y) ≡ a=y]
correct
incorrect
(∀y)[f(a)=f(y) ≡ a=y]
correct
incorrect
(∀y)[f(a)=f(y) ≡ f(a)=y]
correct
incorrect
(∀y)[f(a)=f(y) ≡ f(a)=f(y)]
correct
incorrect
*
not completed
.
Which of the following propositions is derivable from the given premises in F?
1. (∀x)(∀y)[f(x)=f(y) ≡ x=y]
2. Ja • ~Jb
(∃x)(∃y)f(x)≠f(y)
correct
incorrect
(∃x)(∃y)f(x)=f(y)
correct
incorrect
a=b
correct
incorrect
(∀x)a=x
correct
incorrect
f(a)=f(b)
correct
incorrect
*
not completed
.
Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∀x)[Lx ⊃ (~Mx ≡ Nx)]
2. (∃x)[Lf(x) • Mf(x)]
(∃x)[Lf(f(x)) • Mf(f(x))]
correct
incorrect
Lf(f(a)) • Mf(f(a))
correct
incorrect
Lf(e) • Mf(e)
correct
incorrect
La ⊃ (~Ma • Na)
correct
incorrect
Lf(a) ⊃ (~Ma ≡ Na)
correct
incorrect
*
not completed
.
Which of the following propositions is derivable from the given premises in F?
1. (∀x)[Lx ⊃ (~Mx ≡ Nx)]
2. (∃x)[Lf(x) • Mf(x)]
(∀x)(Lx ⊃ ~Nx)
correct
incorrect
(∃x)(Lx • Nx)
correct
incorrect
(∃x)(Mx • Nx)
correct
incorrect
(∃x)Nx
correct
incorrect
(∃x)~Nx
correct
incorrect
*
not completed
.
Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∀x)(∀y)(∀z)[f(x,y)=z ⊃ z=h(b)]
2. f(a,c)=b
3. f(a,b)=c
f(a,f(a,b))=c
correct
incorrect
f(b)=f(c)
correct
incorrect
(∀y)(∀z)[f(x,y)=z ⊃ z=b]
correct
incorrect
(∀y)(∀z)[f(a,y)=z ⊃ z=b]
correct
incorrect
(∀y)(∀z)[f(a,y)=z ⊃ z=h(b)]
correct
incorrect
*
not completed
.
Which of the following propositions is derivable from the given premises in F?
1. (∀x)(∀y)(∀z)[f(x,y)=z ⊃ z=h(b)]
2. f(a,c)=b
3. f(a,b)=c
(∀x)(∀y)f(x,y)=f(y,x)
correct
incorrect
(∀x)(∀y)(∀z)[f(x,y)=z ⊃ f(x,z)=y]
correct
incorrect
f(b)=f(c)
correct
incorrect
h(b)=h(c)
correct
incorrect
b=c
correct
incorrect
*
not completed
.
Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∀x){Px ⊃ [Qf(x)x • Qxf(x)]}
2. Pa • a=f(b)
Pa ⊃ [Qf(a)a • Qaf(a)]
correct
incorrect
Pa ⊃ (Qaa • Qaa)
correct
incorrect
Pb ⊃ [Qf(a)b • Qbf(a)]
correct
incorrect
Pb
correct
incorrect
f(a)=b
correct
incorrect
*
not completed
.
Which of the following propositions is derivable from the given premises in F?
1. (∀x){Px ⊃ [Qf(x)x • Qxf(x)]}
2. Pa • a=f(b)
Qbb
correct
incorrect
Qf(a)f(b) • Qf(b)f(a)
correct
incorrect
Qaf(b) • Qf(b)a
correct
incorrect
Qaa • Qbb
correct
incorrect
Qf(f(a))a • Qaf(f(a))
correct
incorrect
*
not completed
.
Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∀x)[Ax ⊃ x=f(j)]
2. (∀x)f(x)=g(x,a)
3. Ae • Af(e)
f(x)=g(a,a)
correct
incorrect
f(e)=g(e,a)
correct
incorrect
f(e)=g(f(e),a)
correct
incorrect
Ae ⊃ e=j
correct
incorrect
Aj ⊃ j=j
correct
incorrect
*
not completed
.
Which of the following propositions is derivable from the given premises in F?
1. (∀x)[Ax ⊃ x=f(j)]
2. (∀x)f(x)=g(x,a)
3. Ae • Af(e)
(∃x)Ag(f(x),a)
correct
incorrect
(∃x)Ag(a,f(x))
correct
incorrect
Aj
correct
incorrect
e≠f(e)
correct
incorrect
f(e)≠g(f(e),a)
correct
incorrect
*
not completed
.
Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. Da • (∀x)[Dx ⊃ x=f(b)]
2. (∀x)[Ef(x) ≡ Ff(x)]
3. (∀x)(Dx ⊃ Ex)
Df(a)
correct
incorrect
Db
correct
incorrect
Da
correct
incorrect
Ea ≡ Fa
correct
incorrect
Ea ⊃ Da
correct
incorrect
*
not completed
.
Which of the following propositions is derivable from the given premises in F?
1. Da • (∀x)[Dx ⊃ x=f(b)]
2. (∀x)[Ef(x) ≡ Ff(x)]
3. (∀x)(Dx ⊃ Ex)
(∃x)Fx
correct
incorrect
(∀x)(Ex ⊃ Fx)
correct
incorrect
Df(a)
correct
incorrect
(∃x)(Dx • Fx)
correct
incorrect
f(a)=f(b)
correct
incorrect
*
not completed
.
Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∃x)(∃y){Jx • Jy • (∀z)[Jz ⊃ (z=x ∨ z=y)] • Kxf(x) • Kyf(y)}
2. Ja • a=f(b)
Jb
correct
incorrect
Ja • b=f(a)
correct
incorrect
(∃y){Ja • Jy • (∀z)[Jz ⊃ (z=a ∨ z=y)] • Kaf(a) • Kyf(y)}
correct
incorrect
(∃y){Jm • Jy • (∀z)[Jz ⊃ (z=m ∨ z=y)] • Kmf(m) • Kyf(y)}
correct
incorrect
Ja • Jb • (∀z)[Jz ⊃ (z=a ∨ z=b)] • Kaf(a) • Kbf(b)
correct
incorrect
*
not completed
.
Which of the following propositions is derivable from the given premises in F?
1. (∃x)(∃y){Jx • Jy • (∀z)[Jz ⊃ (z=x ∨ z=y)] • Kxf(x) • Kyf(y)}
2. Ja • a=f(b)
Kf(b)f(b)
correct
incorrect
Kf(b)f(f(b))
correct
incorrect
Kaa
correct
incorrect
(∃x)(∃y)(∃z)(Jx • Jy • Jz • x≠y • x≠z • y≠z)
correct
incorrect
(∃x)[Jx • (∀y)(Jy ⊃ y=x)]
correct
incorrect
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