Logic Theory —Basic Notation

Which means that variables, as we’re used to seeing them since algebra, is a no-no in logic theory; not at least without some modification.The bolded statement above is not considered a premise as x could be 5 or 25, making the statement true or false, but currently neither..This, however, doesn’t mean that we have to delete variables from our tool set altogether..There is a way to make use of variables; the process is called quantifying, a clever way of notating bounds on unknown variables in logic..Take a look at the following, updates statement — is this now a premise?for all x, x is larger than one hundredNow that we’ve defined the universe, or domain, of the variable, the statement is no longer ambigious — it’s now a premise as it evaluates to categorically false..The use of this “for all x” is known in logic theory as applying a quantifier..There are two main types of quantifiers..The first, which we’ve just seen, is aptly named the universal quantifier..Dictated by an upside down “A”, ∀, it’s easy to remember that it stands for All or every possible instance within the universe of the statement made..Inspect this second alteration:there exists an x larger than one hundredOnce again without removing the variables we’ve found a way to convert a statement into a premise by applying a quantifier as the statement now evaluates strictly to true..This second type of quantifier is known as the existential quantifier..Notated by a backwards “E”, ∃, it usually reads as “there exists” or “there is.” Both quantifiers are summarized below:On To Truth TablesNow with basic notation out of the way, it’s time to leap to an elementary form of application through truth tables..In the next part, we’ll start by first defining equivalency in logic; in order to use truth tables to analyze which, if any, of the four conditionals we introduced are equal to each other.. More details