Logic
| Logic Symbol |
English Meaning |
Example |
| $\wedge$ |
Conjunction |
p $\wedge$ q |
| p and q. |
|
|
| $\vee$ |
Inclusive Disjunction |
p $\vee$ q |
| p or q. |
|
|
| $\neg$ |
Not |
$\neg$p |
| not p. |
|
|
| $\oplus$ |
Exclusive Or (xor) |
p $\oplus$ q |
| p exclusive or q. |
|
|
| $\implies$ |
Implies |
p $\implies$ q |
| p implies q. |
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| $\iff$ |
Bi–conditional / if and only if (iff) |
p $\iff$ q |
| p iff q. |
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Number Sets
| Number Set Symbol |
English Meaning |
Example |
| $\mathbb{N}$ |
Natural Numbers |
{1, 2, 3, 4,…} |
| $\mathbb{Z}$ |
Integers |
{-2, -1, 0, 1, 2…} |
| $\mathbb{Z}^+$ |
Positive Integers |
{1, 2, 3, 4…} |
| $\mathbb{Q}$ |
Rational Numbers |
{1/2, 1/4, 7/123…} |
| $\mathbb{R}$ |
Real Numbers |
{2.5, $\pi$, 3.3333, …} |
| $\mathbb{C}$ |
Complex Numbers |
$2 + 3 i$ |
Quantifiers
| Qualifier Symbol |
English Meaning |
Example |
| $\isin$ |
Belongs To |
|
| Is In |
$n\in\mathbb{N}$ |
|
| n is in the natural numbers. |
|
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| $\forall$ |
For All |
$\forall n\in\Z$ |
| For all n in the integers. |
|
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| $\exists$ |
There Exists |
|
| For Some |
$\exists \;n \text{ such that }m > n$ |
|
| There Exists an n such that m is greater than m. |
|
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Sets
| Symbol |
English Meaning |
Example |
| $ |
S |
$ |
| \newline |
|
|
| S |
= 3$ |
|
| The cardinality of Set $S$ is 3. |
|
|
| $\isin$ |
Is In/Belongs To |
$n \isin \mathbb{N}$ |
| $n$ is in the natural numbers. |
|
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| $\notin$ |
Is Not In/Does Not Belong To |
$n \notin \mathbb{Z}$ |
| $n$ is not in the integers. |
|
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| $\emptyset$ or {} |
Empty Set |
Self-Explanatory. |
| $\subseteq$ |
Subset |
$A$ $\subseteq$ $B$ |
| A is a subset of B. |
|
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| $\subset$ |
Proper Subset |
$C$ $\subset$ $D$ |
| C is a proper subset of D. |
|
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| $P(S)$ |
|
|
| S being some set |
Power Set |
$P(A)$ |
| Power Set of A. |
|
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| $\cup$ |
Union |
$A$ $\cup$ $B$ |
| A union B. |
|
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| $\cap$ |
Intersection |
$C$ $\cap$ $D$ |
| C intersection D. |
|
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| $-$ |
Difference |
$A$ $-$ ****$B$ |
| A difference B. |
|
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| $\times$ |
Cross Product |
$C$ $\times$ $D$ |
| C cross D. |
|
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Set Builder Notation
<aside>
💡 In set builder notation, elements are defined as variables (which may be written in a certain form). Then, the variable is followed by a | (which means “such that”) and a rule.
</aside>
