Chapter 9, Level 2 Self Quiz: G1

. Choose the correct translation of the following statement.

Some vegans are both healthy and fast. ( Vx: x is a vegan; Hx: x is healthy; Fx: x is fast )

( ∃x )[ Vx ⊃ ( Hx • Fx ) ]

( ∃x )[ Vx • ( Hx ⋅ Fx ) ]

( ∃x )[ Vx • ( Hx ⊃ Fx ) ]

( x )[ Vx • ( Hx • Fx ) ]

. Choose the correct translation of the following statement.

Not all healthy vegans are fast. ( Vx: x is a vegan; Hx: x is healthy; Fx: x is fast )

( x )[ ( Vx • Hx ) ⊃ Fx ]

( x )[ ~ ( Vx • Hx ) ⊃ Fx ]

~ ( x )[ ( Vx • Hx ) • Fx ]

~ ( x )[ ( Vx • Hx ) ⊃ Fx ]

. Choose the correct translation of the following statement.

Not all friends of vegans are vegans. ( Vx: x is a vegan; Gxy: x is a friend of y )

~ ( x ) { ( ∃y ) [ ( Vy • Gxy ) ≡ Vx ] }

( x ) { ( ∃y ) [ ( Vy • Gxy ) ⊃ ~ Vx ] }

~ ( x ){ ( ∃y ) [ ( Vy • Gxy ) ⊃ Vx ] }

~ ( x ){ ( y ) [ ( Vy • Gxy ) ⊃ Vx ] }

. Choose the correct translation of the following statement.

Not all friends and family members of vegans are vegans. ( Vx: x is a vegan; Gxy: x is a friend of y; Fxy: x is a family member of y. )

( x ){~ ( ∃y ) [ Vy • ( Gxy v Fxy ) ] ⊃ Vx }

~ ( x ){ ( ∃y ) [ Vy ⊃ ( Gxy v Fxy ) ] ⊃ Vx }

~ ( x ){ ( ∃y )[ ~ ( Vy • ( Gxy v Fxy ) ] ⊃ Vx }

~ ( x ){ ( ∃y )[ ( Vy • ( Gxy v Fxy ) ] ⊃ Vx }

. Choose the correct translation of the following statement.
Children who have either brothers or sisters are lucky. ( Cx: x is a child; Bxy: x is the brother of y; Sxy: is the sister of y; Lx: x is lucky. )

( x ){ [ Cx • ( ∃y ) ( Bxy v Sxy ) ] ⊃ Ly }

( ∃x ) { [ Cx • ( ∃y ) ( Bxy v Sxy ) ] ⊃ Ly }

( x ) { [ Cx ⊃ ( ∃y ) ( Bxy v Sxy ) ] ⊃ Ly }

( ∃x ) { [ Cx • ( ∃y ) ( Bxy ⊃ Sxy ) ] ⊃ Ly }

. Choose the correct translation of the following statement.

No president has more friends than George Washington. ( Px: x is a president; Fxy: x has more friends than y; g: George Washington. )

~ ( ∃x ) ( Px • Fxg )

~ ( x ) ( Px • Fxg )

~ ( ∃x ) ( Px ⊃ Fxg )

~ ( x ) ( Px ⊃ Fxg )

. Choose the correct translation of the following statement.

No child is a cynic, but some adults are. (Cx: x is a child; Nx: x is a cynic; Ax: x is an adult)

~ ( ∃x ) ( Cx • Nx ) ⊃ ( ∃x ) ( Ax • Nx )

~ ( ∃x ) ( Cx • Nx ) • ( ∃x ) ( Ax • Nx )

~ ( ∃x ) ( Cx • Nx ) • ( x ) ( Ax • Nx )

~ ( ∃x ) ( Cx • Nx ) • ~ ( ∃x ) ( Ax • Nx )

. Choose the correct translation of the following statement.

Some children love everyone. ( Cx: x is a child; Lxy: x loves y )

( x ) ( Cx • ( y )Lxy )

( ∃x ) ( Cx ≡ ( y )Lxy )

( ∃x ) ( Cx • ~ ( y )Lxy )

( ∃x ) ( Cx • ( y )Lxy )

. Choose the correct translation of the following statement.

Johannes Climacus is Søren Kierkegaard. ( c, k )

c k

c • k =

c = k

c ≠ k

. Choose the correct translation of the following statement.

Douglas Adams wrote The Hitchhiker's Guide to the Galaxy. ( Wxh: x wrote The Hitchhiker's Guide to the Galaxy; a: Douglas Adams)

(∃x) Wxh • (y) (Wyh ⊃ y = x ) • x = a

(∃x) [ Wxh • (y) (Wyh ⊃ y = x ) • x = a ]

(∃x) [ Wxh • (∃y) (Wyh ⊃ y = x ) • x = a ]

(∃x) [ Wxh • (y) Wlyh ⊃ ( y = x • x = a ) ]

. Choose the correct translation of the following statement.

No dog except Joseph K. Dogovitch is on trial. ( Dx: x is a dog; Tx: x is on trial; j: Joseph K. Dogovitch. )

Dj • Tj • (x) [ ( Dx • Tx ) ⊃ x = j ]

Dj • Tj (∃x) ( Dx • Tx ) ⊃ x = j

Dj • Tj • (∃ x) [ ( Dx • Tx ) ⊃ x = j ]

Dj • Tj • (x) [ Dx • Tx ⊃ x = j ]

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