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# Lesson 11.10: Logic and Set Theory

## Explanation

Some of the basic symbols used in logic and set theory were covered in an earlier lesson. However, there are multiple symbols that often have the same meaning used in more advanced mathematics topics. Such symbols will be covered in this section.  However, many of the symbols will not be explained in as much detail since the basic use of these symbols has previously been explained.

In logic and set theory the phrases such as "not p" are frequently used. In previous sections the notation used was tilde p or ~p.

### Listed below are additional notations for "not p."

$~p$
⠈⠱⠏

$-p$
⠤⠏

$\stackrel{‾}{p}$
⠏⠣⠱⠻

$p\text{'}$
⠏⠄

### both p and q

$p\wedge q$
⠏⠈⠩⠟

$p·q$
⠏⠡⠟

$p&q$
⠏⠸⠯⠟

### not p or q

$p|q$
⠏⠳⠟

$p/q$
⠏⠸⠌⠟

### neither p or q

$p↓q$
⠏⠫⠩⠒⠒⠕⠀⠟

$p\Delta q$
⠏⠨⠠⠙⠟

### if p then q

$p\therefore q$
⠏⠀⠠⠡⠀⠟

$p
⠏⠀⠐⠅⠀⠟

$p\subset q$
⠏⠀⠸⠐⠅⠀⠟

### if and only if

$↔$
⠫⠪⠒⠒⠕

$\equiv$
⠸⠇

$~$
⠈⠱

$\mathrm{iff}$
⠊⠋⠋

### either p or q but not both

$p\oplus q$
$p⊻q$