Negation and the Not Connector

In the previous post, we have discussed compound propositions. We learned that compound proposition is a proposition formed from simple propositions using some logical connectors. The first logical connector that we are going learn is about “not” which is used for negation.

The negation of a proposition p denoted by ~p (read as “not p”) and is defined by the following truth table. As we can see, if p is true, then ~p is false. If p is false, then ~p is true.

Consider the following negations.

Example 1
q: I am going to the party.
~q: I am not going to the party.

Example 2
r: John is wealthy.
~r: John is not wealthy.  Continue reading…

 

Introduction to Compound Propositions

In the previous post, we have learned about propositions. We learned that propositions are statements that are either true or false but not both. In this post, we are going to combine two or more propositions using words such as and, or, and if and then. Two or more propositions combined are called compound propositions and the words used to combined them are called logical connectors. We formalize our knowledge about compound propositions by the following definition.

Definition

A compound proposition is a proposition formed from simpler propositions using logical connectors or some combination of logical connectors. Some logical connectors involving propositions p and/or q may be expressed as follows: not p, p and q, p or q, if p then qContinue reading…