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What Is a Logic Statement?

Statements provide the foundation for drawing valid conclusions in logic, but mathematics and philosophy also use logic statements for constructing valid arguments and drawing conclusions. Even though it might not seem like it when you're outside of a classroom, you use logic statements in everyday language to relay information to other people and to draw your own conclusions.

Logic Statements
- A statement is a sentence that declares something and that can be verified as either true or false. Sentence fragments, questions and commands aren't logic statements because they aren't declarative, complete sentences.
  
  For example, "The car keys are in the drawer" is a logic statement because it's a complete sentence and declares something that can be verified as true or false. You can check to see if something is a logic statement by adding "It is true that..." to the beginning of the sentence. If it still makes sense with "It is true that..." in front of it, it's a logic statement
Conditional Statement
- A conditional logic statement is a statement that's made up of two conditions, where one condition depends on the other. For the whole conditional statement to be true, the dependent condition must be true when the other is true For example, consider the following conditional statement: "If I study, then I will get a good grade." If you study and get a good grade, then the conditional statement is true; however, if you study and you don't get a good grade, then the conditional statement is false.
Use of Logic Statements
- Statements in logic are used to draw valid conclusions. A conclusion is valid if all of the premises leading up to that conclusion are true. For example, consider the following statements:
  
  "If I study, I will receive a good grade."
  
  "I studied."
  
  If you assume that studying guarantees a good grade, making the first premise true, and that you did study, making the second premise true, then you can conclude that you received a good grade.
Other Considerations
- Variables are often used to easily see the relationship between two logic statements without having to rewrite the entire statement every time you want to talk about the relationship between the two. To do this, you have to assign variables to each of the statements. From the example in Section 3, the two statements being made are: "I study" and "I will receive a good grade." Let P equal "I study" and Q equal "I will receive a good grade":
  
  If P, then Q
  
  P, therefore, Q.

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