PHI 103 test 2

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No alligators are non-turtles

All alligators are turtles

Infer the missing statement All dogs are turtles All cats are dogs ∴(..............)

All cats are turtles

Fluffy is a cat

All members of the class of Fluffy are cats

Any sound argument is valid

All sound arguments are valid

All unsound arguments are invalid

All valid arguments are sound

J if and only if it is not the case that K if L

J↔~(L→K)

All sound arguments are invalid

none

Both P if Q and R only if S

none of these

P only if it is not the case that Q if and only if not R

none of these

Some non-alligators are not non-turtles

none of these

Some R are non Q

one of these

If not both A and B, then C only if D

~(A&B)→(C→D)

If it is not the case that either J or K, then it is not the case that both P and Q

~(JvK)→~(P&Q)

J, if it is not the case that either K or not L

~(Kv~L)→J

It is not the case that if P, then Q

~(P→Q)

Either not A or it is not the case that either B or C

~Av~(BvC)

It is not the case that both not A and not B if not C

~C→~(~A&~B)

s is not P

~Ps

If it is not the case that P, then Q

~P→Q

not P if not Q

~Q→~P

Some S are not non-P

(∃x)(Sx&Px)

Either P and Q or R if and only if S

(P&Q)v(R↔S)

Either P if and only if Q or R

(P↔Q)vR

No P are Q

(x)(Px→~Qx)

All P are non-S

(x)(Px→~Sx)

If not A and not B, then it is not the case that both C and D

(~A&~B)→~(C&D)

If not P and not Q, then not R

(~P&~Q)→~R

Some P are not S

(∃x)(Px&~Sx)

Read the following instance: All poodles are mice No mice are cats No cats are poodles How should we rewrite the first premise to put the argument in standard logical form?

All P are M

A unless it is not the case that B if C

Av~(C→B)

A only if B

A→B

A only if it is not the case that either A or not B

A→~(Av~B)

If A, then it is not the case that B if not C.

A→~(~C→B)

Read the following argument: Some poodles are cats and no cats are dogs so some poodles are not dogs Identify the first premise in this argument

No cats are dogs

Infer the missing statement (........................) Some cats are furballs ∴Some cats are not dogs

No dogs are furballs

Fido is not a cat

No members of the class of Fido are cats

P unless ~Q

Pv~Q

Infer the missing statement Some cats are not furballs All cats are cute animals ∴(.................)

Some cute animals are not furballs

Infer the missing statement (.................) All dogs are cats ∴Some cats are elephants

Some dogs are elephants

Some non-cats are not non-dogs

Some dogs are not cats

Few sound arguments are invalid.

Some sound arguments are not valid

Many non-alligators are not non-turtles

Some turtles are not alligators

Infer the missing statement All dogs are cats (....................) ∴Some turtles are not dogs

Some turtles are not cats

Some valid arguments are unsound

Some valid arguments are not sound

Some valid arguments are not unsound

Some valid arguments are sound


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