Introduction to Logic solution – Translate syllogistic arguments into standard form

EXAMPLE 2

Some metals are rare and costly substances.

no welder’s materials are nonmetals.

some welder’s materials are rare and costly substances.

 

some m is p.

no s is non-m. all s is m.

some s is p.

 

IAI-1

Invalid.

 

EXAMPLE 3

all belligerents were allies either of Germany or Britain.

some Asian nations were not allies of either Germany or Britain.

Some Asian nations were nonbelligerents.

 

all p is m.

some s is not m.

some s is non-p. some s is not p.

 

AOO-2

valid.

 

EXAMPLE 4

some people in perfect physical condition are not nonathletes.

no drinkers are persons in per-fect physical condition.

Some nondrinkers are athletes.

 

some m is not non-p. some m is p.

no s is m. all s is non-m. all m is non-s.

some non-s is p

 

IAI-3

valid.

 

EXAMPLE 5

all explosives are flammable things.

All things inflammable are unsafe things.

all things that are safe are nonexplosives.

 

all p is m.

all m is non-s. no m is s.

all s is non-p. no s is p.

 

AEE-4

valid.

 

EXAMPLE 6

no material things are unchangeable things.

no worldly goods are things immaterial.

All worldly goods are changeable things.

 

no m is non-p. all m is p.

no s is non-m. all s is m.

all s is p.

 

AAA-1

invalid.

 

EXAMPLE 7

All those who are neither members nor guests of members are those who are excluded.

all those who are included are conformists.

no nonconformists are either members or guests of members.

 

all non-p is non-m. all m is p.

all m is non-s. all s is non-m. no s is m.

no s is p.

 

AEE-1

Invalid.

 

EXAMPLE 8

no humans are immortals.

All mortals are imperfect beings.

all perfect beings are nonhumans.

 

no p is non-m. all p is m.

all m is non-s no m is s.

all s is non-p. no s is p.

 

AEE-4

valid.

 

EXAMPLE 9

all visible objects are absent things.

All things present are nonirritants.

no irritants are invisible objects.

 

all p is non-m. no p is m.

all m is non-s. no m is s.

no s is non-p. all s is p.

 

EEA-4

Invalid.

 

EXAMPLE 10

no objects over six feet long are easy things to store.

all difficult things to store are useless things.

All useful things are objects no more than six feet long

 

no p is non-m. all p is m.

all m is non-s. no m is s.

all s is non-p. no s is p.

 

AEE-4

valid.

 

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