# Logic and Proof

### Topics

## Introduction to :

**Mathematical statements** are exactly the same as fashion statements. Except instead of clothes, we have mathematical formulas. Hopefully we won't get chilly walking down the runway.

The simplest kind of mathematical statement is an explanation of how numbers are related. For example, you might say, "*x* = 5" or, "4 + 7 = 35" or, "58 is the sum of two prime numbers." As you can see, some statements are true, some are false, and some are as clear as a mud smoothie.

What all of these statements have in common is that they can't be split into simpler statements—they are *indivisible* (with liberty and justice for all). The Greek word for indivisible is *atomos*, so we call these statements **atoms**. Unlike the atoms in chemistry, mathematical atoms can make only statements, not bombs.

#### Example 1

Does any value of |

#### Example 2

Does any food satisfy, "This food is a pie or it tastes like a blueberry"? |

#### Example 3

Is there any value of |

#### Exercise 1

Sandra loves skydiving, pepperoni pizza, and the number 17. She doesn't like Tuesdays or the color purple (sorry, Alice Walker). Is the statement "Sandra loves pepperoni pizza and she loves Tuesdays" true?

#### Exercise 2

Sandra loves skydiving, pepperoni pizza, and the number 17. She doesn't like Tuesdays or the color purple (sorry, Alice Walker). Is the statement "Sandra loves 17 or she does not love 17" true?

#### Exercise 3

Sandra loves skydiving, pepperoni pizza, and the number 17. She doesn't like Tuesdays or the color purple (sorry, Alice Walker). Is the statement "Sandra does not love purple or she loves skydiving" true?

#### Exercise 4

Is there a value for *x* that will satisfy the statement "*x* = 7 or *x*^{2} = 25"?

#### Exercise 5

Is there a value that will satisfy the statement "*x*^{0} = 1 and *x* + 1 = 4,623"?