Symbolic Logic I
Identifying Statement Forms
There are six primary statement forms in Propositional Logic. They are:
Example: The plants need watering.
Simple statements express one idea.
Example: A Republican is in the White House and the Democrats control the Senate.
Conjunctions are compound statements made up of two or more statements (which
may be either simple or compound) connected with the word "and"
(other conjunctive words are "but", "yet", "although", "also"...). The two simple
statements in the example
above are: "a Republican is in the White House" and "the Democrats control the Senate".
The components of the conjunction are called conjuncts. Each
conjunct may be either simple or compound
Example: Either the Red Sox or the Yankees will win the pennant.
Disjunctions are compound statements made up of two or more statements (simple
or compound) connected with such words
as "either...or", "or", "unless". The two simple statements 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.
Example: If tuition goes up, then I'll have to get another job.
Conditionals are compound statements made up of two or more statements (simple
or compound) connected by such "hypothetical" terms as "if...then", "implies that", "provided that",
"only if", "is implied by". The two simple statements 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 statement 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.
Example: The final exam will include Chapter 5 if, and only if, we cover it in class.
Biconditionals are compound statements made up of two components (simple or
compound), where each component is said to imply
the other. The two components that make up the statement above are: "The final exam will include Chapter
5" and "We cover Chapter 5 in class". The example above could be expanded to
read "If we cover chapter 5 in class, then it will be on the final exam and
chapter 5 will be on the final exam only if we cover it in class." The
expanded version is a conjunction of 2 conditionals, which is why this statement
form is called 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.
Example: It is false that money is the root of all evil.
A negation is any statement denying that another statement is true. Simple
statements can be denied/negated just
as compound statements can be denied. Here is an example of a negated conjunction: Lisa and Earl won't both go to the movies.
What this statement 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 statement: "it is false
that", "it is not the case that", "won't", "can't", "unsuccessful".
Identify the form of the statements below. Possible identifications are: Simple,
Conjunction, Disjunction, Conditional, Biconditional, Negation of a
simple statement, 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.
- 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