MACM 101 Chapter Notes - Chapter 2.4: Universal Quantification, Logical Consequence, Counterexample
15 Mar 2016
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From section 2. 1, we know that a variable such as x are not statements. For example x+2 is an even integer is not true or false until we substitute a value in for x. We refer to this sentence as an open statement. Deinition: open statement: contains one or more variables, it is not a statement, but, becomes a statement when the variables in it are replaced by a certain allowable choice. Remember: the number x + 2 is an even integer is an open statement that contains the single variable x. In the above deinition we restricted the certain allowable choices to integers. These allowable choices are what is called the universe or universe of discourse for the open statement. The universe comprises the choices we wish to consider for the variable(s) in the open statement: the universe is an example of a set.
