Examples of Logical Inference

This page contains many examples of logical inferences. Most of them are collected from various books or other sources. Others are my own design.

Examples of Propositional Logic

1. Cable TV are broadcasting violent movies. Cable TV companies do not have the right to let children watch violent movies. Therefore, cable TV should not broadcast violent movies.

Examples of Predicate Logic

1. All fruit is tasty if it is not cooked. This apple is not cooked. Therefore, it is tasty.
2. All fruit is tasty if it is not cooked. This apple is cooked. Therefore, it is not tasty.
3. Some fruit is tasty if it is not cooked. This apple is cooked. Therefore, it is not tasty.
4. Some fruit is tasty if it is not cooked. This apple is not cooked. Therefore, it is tasty.
5. All that glistens is not gold. This pot does not glisten. Therefore, it is gold.
6. No lecturer who spends her time writing books on logic or who devotes herself to her students will come to the notice of the establishment. No one who does not come to the notice of the establishment will secure preferment. Therefore, no lecturer who spends her time writing books on logic will secure preferment.
7. Some lecturers are imaginative but poor communicators. Only good students are lecturers. Good students are not imaginative. Every artist is imaginative. Therefore, not every good student is an artist.
8. Dilly loves all and only those who love Milly. Milly loves all and only those who do not love Dilly. Dilly loves herself. Therefore, Milly loves herself.
9. All those who honor both their parents are blessed. If anyone dislikes any of his siblings he does not honor his parents. Jack likes his sister, Jill. Therefore Jack is blessed.
10. All lecturers are determined. Anyone who is determined and intelligent will give satisfactory service. Clare is an intelligent lecturer. Therefore Clare will give satisfactory service.
11. All men are motal. Socrates is mortal. Therefore Socrates is a man.
12. All men are mortal. Socrates is a man. Therefore Socrates is mortal.
13. Every student likes logic. If a person likes logic and studies hard, she will pass all her exams. Joann is a lover of logic who studies hard. Therefore, Joann will pass her tomorrow's exam.
14. Some musician are writers. Some mathematicians are not writers. Therefore, some mathematicians are not musicians.
15. Some people like everybody who supports the president. Everybody likes someone who supports the president. Anybody who likes somebody who supports the president does not herself support the president. Therefore, the president does not support herself.
16. Some students are anxious. Some students study. If a student is anxious he will not pass his exam unless he studies. Therefore, no students will pass their exams.
17. Some students are anxious. Some students study. If a student is anxious he will not pass his exam unless he studies. Therefore, some students will pass their exams.
18. Some students are anxious. All students study. If a student is anxious he will not pass his exam unless he studies. Therefore all students will pass their exams.
19. All students are anxious. Some students study. If a student is anxious he will not pass his exam unless he studies. THerefore, some students will pass their exams.
20. Some students attend logic lectures diligently. No student attends boring logic lectures diligently. Sean's lecture on logic are attended diligently by all studnets. Therefore none of Sean's logic lectures are boring.
21. If one number is less than or equal to a second number, and the second number is less than or equal to a third, then the first number is not greater than the third. A number is less than or equal to a second number if and only if the second number is greater than the first or the first is equal to the second. Given any number, there is another number that it is less than or equal to. Therefore, every number is less than or equal to itself.
22. 讀書的目的是避免愚昧，而愚昧是一切痛苦的根源•所以多讀書可以減少痛苦•

Examples of Puzzles

1. Suppose we know the following facts: if A is not guilty then B and C are guilty. At least one of B and C is not guilty. Either A is not guilty or B is guilty. So who is guilty? (Answer: A and B are guilty; C is not.)
2. Suppose we know the following facts: If A is blue then B is yellow. If A is yellow then B is red. If B is not blue then C is yellow. If C is red then A is blue. So what are the colors of A, B, and C?

Examples of Fun Stories

1. The ears of grasshoppers are on their legs.
2. The lady says, "anything is fine with me."

Examples of Fallacies

1. 甲：我的意見才對。乙：為什麼？甲：因為我是權威。乙：為什麼你是權威？ 甲：因為我的意見永遠是對的。 (circular reasoning)
2. 誰也不能證明神明不存在，所以一定有神明。 (shift the burden of proof)
3. 我認為這個化石是長毛象的牙齒。如果有人不同意，就請他提出證明來。 (shift the burden of proof)
4. 你的意見不對。因為沒有人會相信。 (shift the burden of proof)
5. 龜山島的信天翁即將絕種。有人反對加以保護，他說：我們是否要保護所有瀕臨絕 種的生物? (shift the burden of proof)
6. 沒有人因為吃搖頭丸而死。所以搖頭丸可以吃。 (force the listener to choose one of two alternatives)
7. 穿著暴露是不道德的。所以在海灘上穿游泳衣是不道德的。(force the listener to choose one of two alternatives)
8. 如果整天玩電玩，你是進不了台大的。電玩和台大，你要選那一樣？ (force the listener to choose one of two alternatives)
9. 現在的鴨嘴獸沒有牙齒，但是古時候的鴨嘴獸有牙齒。現在的麻雀也沒有牙齒。 所以古時候的麻雀應該有牙齒。 (wrong analog)
10. 上次地震來臨之前，螞蟻都會搬家。今天早上我看到螞蟻搬家， 所以地震即將發生。 (generalization)
11. 最近幾年每次地震來臨之前，螞蟻都會搬家。今天早上我看到螞蟻搬家， 所以地震即將發生。 (generalization)
12. 數百年來每次地震來臨之前，螞蟻都會搬家。今天早上我看到螞蟻搬家， 所以地震即將發生。 (generalization, though more convinving)
13. 在破碎的玻璃片旁躺著一隻麻雀，大概破碎的玻璃片對麻雀有致命的吸引力吧。 (因果顛倒)
14. 女生的數學普遍不佳，是因為男生不喜歡精於計算的女生。 (無因果關係)
15. 因為女生的數學普遍不佳，所以女生崇拜數學高手。男生也因此都是數學高手。 (無因果關係)
16. 天氣炎熱的時候，溫度計一定顯示著高溫。所以氣溫是由溫度計來控制。 (因果顛倒)
17. 每個女生都有她的魅力。但也不是沒有缺乏魅力的女生。 (contradiction)
18. 她美得驚人。我不喜歡令人驚訝的人。所以我不喜歡她。 (一字數義，歧義)
19. 考卷上明明寫著：在空格內寫下適當的答案。所以我在每一個空格內寫著： 適當的答案。 (歧義)
20. 考試的時候，神經敏銳是很重要的。害怕的時候神經都很敏銳。所以考試的時候， 不妨去想一些可怕的事。 (歧義)

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