Glossary of terms and notation

\(\in\): "in" or "is an element of." \(x\in R\) means that \(x\) is an element of \(R\).

\(\forall\): "for all." \(\forall x \in R\) means for all elements \(x\) that are in \(R\).

\(\exists\): "there exists."

\(\cup\): "union." \(x\cup y\) is the set that contains all the elements of \(x\) and all the elements of \(y\).

\(\cap\): "intersection." \(x\cap y\) is the set that contains all the elements of \(x\) that are also elements of \(y\).

\(\wedge\): the logical operator "and."

\(\vee\): the logical operator "or."

\(\neg\): "not" or the logical negation.

\(!\): signifies that the object that it is attached to is unique meaning that it is the only object with the given attributes.

\(\rightarrow\): "implies" or the if-then logical operator. \(a\rightarrow b\) is read "if \(a\) then \(b\)" or "\(a\) implies \(b\)."

\(\leftrightarrow\): "if and only if." This is similar to the symbol above, but works in both directions. \(a\leftrightarrow b\) means that \(a\) implies \(b\) and \(b\) implies \(a\).