# Mathematical Proof/Appendix/Symbols Used in this Book

This is a list of all the mathematical symbols used in this book.

${\displaystyle [a,b]}$

Closed interval notation. Signifies the set of all numbers between a and b (a and b included)

${\displaystyle \lor }$

A logical "or" connector. A truth statement whose truth value is true if either of the two given statements is true and false if they are both false. ${\displaystyle P\lor Q}$

${\displaystyle \land }$

A logical "and" connector. A truth statement whose truth value is true only if both of the two given statements is true and false otherwise. ${\displaystyle P\land Q}$

${\displaystyle \lnot }$

A logical "not" unary operator. A truth statement whose value is opposite of the given statement. ${\displaystyle \lnot P}$

{ }

Set delimiters. A set may be defined explicitly (e.g. ${\displaystyle A=\{1,2,3,4\}}$), or pseudo-explicitly by giving a pattern (e.g. ${\displaystyle B=\{2,4,6,8,\ldots \}}$. It may also be defined with a given rule (e.g. ${\displaystyle C=\{x|P(x)\}}$, the set of all x such that P(x) is true).

${\displaystyle \in }$

The "element of" binary operator. This shows element inclusion in a set. If x is an element of A we write ${\displaystyle x\in A.}$

${\displaystyle \subset }$

The "set inclusion" or "subset" binary operator. If all the elements of A are in B, then we say that A is a subset of B and write ${\displaystyle A\subset B.}$ Note that in this book, ${\displaystyle A\subset B}$ when ${\displaystyle A=B.}$

${\displaystyle \cup }$

The union of two sets. A set containing all elements of two given sets. ${\displaystyle A\cup B=\{x|(x\in A)\lor (x\in B)\}.}$

${\displaystyle \cap }$

The intersection of two sets. A set containing all the elements that are in both of two given sets. ${\displaystyle A\cap B=\{x|(x\in A)\land (x\in B)\}.}$