What Logicallyequivalent is
Logically equivalent is a way of comparing two logical statements or propositions to see if they have the same meaning. Logically equivalent statements are also referred to as logically equivalent propositions. Logically equivalent statements have the same truth values (true/false) under all interpretations and assignments of truth values.
Steps for Logically Equivalent:
-
Read both statements carefully and make sure you understand them.
-
Examine the structure of both statements to see if they are the same.
-
See if the two statements have the same logical form, meaning that they can be expressed using the same set of logical operators (AND, OR, NOT, etc.).
-
Compare the truth tables of each statement to see if they are the same.
-
If the truth tables are the same, then the statements are logically equivalent.
Examples
- Two regression models which produce the same predictions but use different independent variables.
- Two sets of data which produce the same mean and variance.
- Two sets of data which produce the same probability distribution.
- Two tests which produce the same p-value.
- Two sets of data which produce the same correlation coefficient.
- Two samples of data which produce the same confidence interval.