Implications and quantifiers. In everyday life and in mathematics we make inferences that adhere to common laws of logic . Definition of a Statement 1 . An open statement is a sentence that contains one or more variables and becomes a statement when each variable is replaced by a specific item from a designated set. Example 1 .
All children are left-handed is a false statement.
Many people enjoy science fiction is a true statement. This sentence is true is not a statement at all since it can be both true and false. It is neither a true nor false statement since this depends upon the replacement for the variable n. In logic we use symbols to represent statements. It is snowing.