Symbolic Logic I  
Identifying Statement Forms

There are six primary statement forms in Propositional Logic. They are:

1. Simple
Example: The plants need watering.
Simple statements express one idea.

 

2. Conjunction
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

 

3. Disjunction
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.

 

4. Conditional
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.

 

5. Biconditional
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.

 

6. Negation
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.

 

The Answers