16.1. And and Or Statements http://www.ck12.org
16.1 And and Or Statements
Here you will use the words “and” and “or” as logical connectives in complex statements. You will also use set
theory and logical notation to diagram logical statements.
The words “and” and “or” are common in everyday language. In mathematics, there are some subtle differences that
you need to watch out for, especially considering the word “or”.
It will rain or it will snow.
When is this statement true and when is it false?
Watch This
Watch the portion of this video focusing on truth tables of conjunction and disjunction:
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/63005http://www.youtube.com/watch?v=_5Z_0824RHw James Sousa: Truth Tables for Compound Statements
Guidance
Anatomic statementis adeclarative statementwithout logical connectives that has a truth value. Here are two
declarative statements:
- P=It is snowing.
- Q=I am cold.
Thetruth valueof a statement is whether the statement is true or false. As a mathematician, your job is to determine
when a logical statement is true and when it is false. If you don’t have enough information to determine whether the
original statements are true or false, you can build a truth table to organize all the possible cases.
Consider the atomic statementPjoined with the atomic statementQ. The following sentence can be written using
the symbol “∨” for the logical connective “or”.
It is snowing or I am cold.
P∨QThis statement is a little strange because it seems to imply that it is always the case that one or both of those atomic
statements is happening. Your common sense may dictate that this statement isn’t true because of course there are
times when it is sunny and you are warm. It’s important to remember that not all statements are true! Your job is to