Identifying Sentences

L o g i c
Identifying Kinds of Sentence

There are six primary types of sentence (or statement, assertion, proposition) in Sentential Logic. They are:

1. Simple

Example: The plants need watering.

Simple sentences express one idea.

2. Conjunction
Example: A Republican is in the White House and the Democrats control the Senate.
Conjunctions are compound sentences made up of two or more simple sentences connected with the word "and" (other conjunctive words are "but", "yet", "although", "also"...). The two simple sentences in this example are: "a Republican is in the White House" and "the Democrats control the Senate".
The components (simples sentences) of the conjunction are called conjuncts.

3. Disjunction
Example: Either the Red Sox or the Yankees will win the pennant.
Disjunctions are compound sentences made up of two or more simple senytences connected with such words as "either...or", "or", "unless". The two simple sentences in this example are: "the Red Sox will win the pennant" and "the Yankees will win the pennant".
The components of the disjunction are called disjuncts.

4. Conditional
Example: If tuition goes up, then I'll have to get another job.
Conditionals are compound sentences made up of two or more simple sentences (this would be the simplest form of a conditional) connected by such "hypothetical" terms as "if...then", "implies that", "provided that", "only if", "is implied by". The two simple sentences in the above example are "tuition will go up" and "I'll have to get another job". A more complicated sort of conditional would be one where the first part is a simple sentence but where the second part is a conjunction, such as: If you like surfing, then you'll like both skiing and skateboarding.
The components of the conditional are called the antecedent and the consequent.

5. Biconditional
Example: The final exam will include Chapter 5 if, and only if, we cover it in class.
Biconditionals are compound sentences made up of two conditionals, where each conditional is said to imply the other. The two conditionals that make up the sentence above are: "If the final exam will include Chapter 5, then we will have covered it in class" and "If we cover Chapter 5 in class, then it will be included on the final exam". In the example above, "if, and only if" is the phrase indicating that the sentence is indeed a biconditional. Other such logical words/phrases include "implies and is implied by", "is a necessary and sufficient condition", "just in case that", "entails".
The components of the biconditional do not have special names.

6. Negation
Example: It is false that money is the root of all evil.
A negation is any sentence denying that another sentence is true. Simple sentences can be denied/negated just as compound sentences can be denied. Here is an example of a negated conjunction: Lisa and Earl won't both go to the movies. What this sentence is actually saying, in other words, is that it is false that Lisa and Earl will both go to the movies. There are many ways to deny/negate a sentence: "it is false that", "it is not the case that", "won't", "can't", "unsuccessful".

Identify the sentences below. Possible identifications are: Simple, Conjunction, Disjunction, Conditional, Biconditional, Negation of a simple sentence, Negated conjunction, Negated disjunction, Negated conditional, Negated biconditional, Double negation.

1. Snow is falling in Cordoba.

2. Time is money and money is freedom.

3. Neither is time money nor is money freedom.

4. That coral is a fragile organism implies that we should not drill offshore for oil.

5. He who lies is eventually caught.

6. Hawai'ian surfers will compete in Australia unless the Aussies win at Pipeline this year.

7. The Navy will take a beating at Jakarta if intelligence is not detailed.

8. Being intelligent is not a sufficient condition for being a teacher.

9. If child molestation is on the rise, then the police should step up operations and follow through.

10. Two out of three 3 couples vacation in climates warmer than their home climates.

11. Since Michigan State is undefeated, Wisconsin must have lost at least one game.

12. Notre Dame and Michigan State will both win provided that Duke and Clemson both lose.

13. Trees still grow in Central Park.

14. Long term prize fighters don't do well at problem solving.

15. A necessary condition for a match to light is friction applied to its surface.

16. If terrorist demands are met, then we'll have slavery or religious intolerance.

17. Neither will the university hire in Physics nor will it seek funding for a physics lab.

18. A necessary and sufficient condition for social personhood is social acceptance.

19. Having a steering wheel in the car isn't a necessary condition for the car's engine to operate.

20. If the trip costs over a thousand dollars, then we won't be able to go; unless we get the grant.

21. Mary won't both learn to drive and learn to sky dive.

22. The university won't either augment the technology budget or fund athletics to add another sport.

23. It is not the case that a necessary and sufficient condition for smoke is fire.

The Answers

1. Simple

2. Conjunction

3. Conjunction (with both conjuncts negated) Also, Negated Disjunction

4. Conditional (with the consequent negated)

5. Conditional ("If anyone lies, he/she will eventually be caught")

6. Disjunction

7. Conditional (the antecedent is "intelligence is not detailed")

8. Negated conditional

9. Conditional (the consequent is a conjunction)

10. Simple

11. Conjunction (might look like a conditional, but 'since' is conjunctive, not hypothetical)

12. Conditional (both antecedent and consequent are conjunctions)

13. Simple

14. Negation

15. Conditional

16. Conditional

17. Conjunction (or Negated Disjunction)

18. Biconditional

19. Negated Conditional

20. Disjunction (the first disjunct is a conditional)

21. Negated Conjunction

22. Negated Disjunction

23. Negated Biconditional