| Symbol | Meaning | Example |
| \(\Rightarrow\) | if...then; implies | \(\abs{x} > 1 ~\Rightarrow~ x^2 > 1\) |
| \(\Leftrightarrow\) | if and only if; two-way implication | \(\abs{x} > 1 ~\Leftrightarrow~ x^2 > 1\) |
| iff | if and only if; two-way implication | \(\abs{x} > 1\) iff \(x^2 > 1\) |
| \(\nRightarrow\) | does not imply | \(\abs{x} > 1 ~\nRightarrow~ x > 1\) |
| \(\exists\) | there exists | \(\exists\) a number \(c > 0\) |
| \(\nexists\) | there does not exist | \(\nexists ~x\) such that \(x^2 < 0\) |
| \(\exists !\) | there exists a unique | \(\exists !~x\) such that \(2x-1=3\) |
| \(\forall\) | for every | \(\forall x \ge 0\), \(\sqrt{x}\) is a real number |
| \(\equiv\) | is identically equal to | \(f \equiv 0 ~\Rightarrow~ f(x)=0\) for all \(x\) |
| \(\propto\) | is proportional to | \(y ~\propto x^2 ~\Rightarrow~ y=kx^2\) for some \(k\) |
| \(\subseteq\) | is a subset of | \(\lbrace 0,1 \rbrace \subseteq \lbrace 0,1,2 \rbrace\) |
| \(\in\) | is an element of | \(1 \in \lbrace 1,2,3 \rbrace\) |
| \(\notin\) | is not an element of | \(1 \notin \lbrace 2,3 \rbrace\) |
| \(\cup\) | union of sets | \(\lbrace 0,1 \rbrace \cup \lbrace 2,3 \rbrace = \lbrace 0,1,2,3 \rbrace\) |
| \(\cap\) | intersection of sets | \(\lbrace 0,1 \rbrace \cap \lbrace 1,2 \rbrace = \lbrace 1 \rbrace\) |
| \(\varnothing\) | empty set | \(\lbrace 0,1 \rbrace \cap \lbrace 2,3 \rbrace = \varnothing\) |
| \(\therefore\) | therefore | \(\therefore\) \(n\) must exist |