What is a Mathematical Statement and What is Logic?

Logic as we know it, means knowledge/thinking. People use logic for everything. You need logic to know how to tie your shoes, to go to school/work, even to cook! We use logic everyday of our lives and that's what makes us different from animals: we have logic.


A Mathematical Statement is a statement that can be said to be true or false. In order to perform a mathematical statement we need logic, and I'm pretty sure all human beings have logic.
                     Ex: Congruent angles are angles that measure the same. T or F

Open Sentences is a mathematical statement where there is a "variable"
                    Ex of Variables: She is pretty. "She" is the variable.


Negations is pretty simple and pretty self explanatory, the name clearly says what is about. Negations is when you deny something and say "not". It always have the opposite truth value. Using negations, you still have to use logic and a mathematical sentence.
                      Ex: An owl is a fish. --> F
                       - Negation: An owl is not a fish. --> T


Conjunction is a word that helps connect two or more sentences.

• "and": both statements must be true for the statement to be true
• "or": either statement (or both) can be true for the statement to be true

There are 4 types of logic in math. In this post we will learn about 2 only.


A Conditional is the most frequently used statement in the construction of an argument or in the study of math.
                      Ex: Today is raining. Tomorrow will be sunny. The conditional of these statements are "If today is raining, then tomorrow will be sunny". So you basically add "If" to the hypothesis and "then" to the conclusion.


An Inverse is formed by negating the hypothesis and the conclusion.
                   Ex: Today is raining. Tomorrow will be sunny. The inverse to these statements are "If today is not raining, then tomorrow will not be cloudy"


Problem:      "A trapezoid is a four sided polygon"
                                   True             or                 False


**Images and some of the examples provided by google.com/images and my notes from Geometry class.