Syllogisms-Which are valid? Correct the invalid ones.
Brain Surgeons save lives.
Marie is a brain surgeon.
Therefore, Marie saves lives.
An English Bulldog is a dog.
All dogs have four legs.
Therefore, English Bulldogs have four legs.
All humans grow.
All children are human.
Therefore, children grow.
I love chocolate.
All brownies are made of chocolate.
Therefore, I love brownies.
Shirts are composed of threads.
Threads are made from cotton.
Therefore, shirts are composed of threads.
Jack is very talented.
Talented people are successful in life.
Therefore, Jack is successful in life.
Kids are energetic.
Susan is energetic.
Therefore, Susan is a kid.
All computers need electricity.
The Dell 500 is a computer.
Therefore, the Dell 500 needs electricity.
Mrs. Shaffer wears glasses that prohibit her from seeing any humans.
She is able to see Mr. Shaffer.
Therefore, Mr. Shaffer is not human.
Students who want to make good grades study.
Michelle studies.
Therefore, Michelle wants to make good grades.
All fruits have seeds.
Cantaloupe have seeds.
Therefore, cantaloupe is a fruit.
All Texans drive trucks.
Brian is a Texan.
Therefore, Brian drives a truck.
It looks like a few are quite wrong that you missed. Let me give you one example:
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Students who want to make good grades study.
Michelle studies.
Therefore, Michelle wants to make good grades.
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What if Michelle studies because her parents force her to?
Corrected, it would say Michelle wants good grades. Therefore, Michelle studies.
Brain surgeons save lives
Marie is a brain surgeon,
Therefore, Marie saves lives.
This would be correct, if the first premise would include the word"all"
All brain surgeons save lives,
Marie is a brain surgeon,
Therefore, Marie saves lives.
The valid syllogisms are:
1. Brain Surgeons save lives.
Marie is a brain surgeon.
Therefore, Marie saves lives.
Explanation: This is a valid syllogism because it follows the logical form known as "affirmative categorical syllogism," where the middle term ("brain surgeon") is distributed in both premises.
2. All humans grow.
All children are human.
Therefore, children grow.
Explanation: This is a valid syllogism because it follows the logical form known as "universal affirmative syllogism," where the middle term ("human") is distributed in the major premise.
3. Shirts are composed of threads.
Threads are made from cotton.
Therefore, shirts are composed of threads.
Explanation: This is a valid syllogism because it follows the logical form known as "transitive syllogism," where the middle term ("threads") is canceled out by being distributed once and undistributed once in the premises.
4. All computers need electricity.
The Dell 500 is a computer.
Therefore, the Dell 500 needs electricity.
Explanation: This is a valid syllogism because it follows the logical form known as "universal affirmative syllogism," where the middle term ("computer") is distributed in the major premise.
The invalid syllogisms are:
1. An English Bulldog is a dog.
All dogs have four legs.
Therefore, English Bulldogs have four legs.
Explanation: This is an invalid syllogism because it commits the logical fallacy known as "undistributed middle term." The middle term ("dog") is not distributed in either premise, so the conclusion cannot be logically inferred.
2. I love chocolate.
All brownies are made of chocolate.
Therefore, I love brownies.
Explanation: This is an invalid syllogism because it commits the logical fallacy known as "illicit major term." The major term ("I love brownies") is undistributed in the major premise, so the conclusion cannot be logically inferred.
3. Jack is very talented.
Talented people are successful in life.
Therefore, Jack is successful in life.
Explanation: This is an invalid syllogism because it commits the logical fallacy known as "illicit major term." The major term ("Jack is successful in life") is undistributed in the major premise, so the conclusion cannot be logically inferred.
4. Kids are energetic.
Susan is energetic.
Therefore, Susan is a kid.
Explanation: This is an invalid syllogism because it commits the logical fallacy known as "undistributed middle term." The middle term ("energetic") is not distributed in either premise, so the conclusion cannot be logically inferred.
5. Mrs. Shaffer wears glasses that prohibit her from seeing any humans.
She is able to see Mr. Shaffer.
Therefore, Mr. Shaffer is not human.
Explanation: This is an invalid syllogism because the conclusion does not logically follow from the premises. The fact that Mrs. Shaffer wears glasses that prohibit her from seeing any humans does not automatically make Mr. Shaffer a non-human.
6. Students who want to make good grades study.
Michelle studies.
Therefore, Michelle wants to make good grades.
Explanation: This is an invalid syllogism because the conclusion does not logically follow from the premises. Just because Michelle studies does not necessarily mean that she wants to make good grades. There could be other reasons for studying.
7. All fruits have seeds.
Cantaloupe have seeds.
Therefore, cantaloupe is a fruit.
Explanation: This is an invalid syllogism because it commits the logical fallacy known as "illicit minor term." The minor term ("cantaloupe is a fruit") is undistributed in the minor premise, so the conclusion cannot be logically inferred.
8. All Texans drive trucks.
Brian is a Texan.
Therefore, Brian drives a truck.
Explanation: This is an invalid syllogism because it commits the logical fallacy known as "undistributed middle term." The middle term ("Texans") is not distributed in either premise, so the conclusion cannot be logically inferred.