MYP Standard Mathematics Sets, Logic and Probability Key Definitions

The cardinality of a set $A$, written $n(A)$, is the number of elements in $A$.

The set of elements not in a set. The complement of $A$ (relative to $U$) is $A'$.

The conditional probability of $B$ given $A$ is
$$P(B\mid A)=\frac{P(A\cap B)}{P(A)}, \quad P(A)>0.$$

For any sets $A$ and $B$ in a universal set $U$,
$$(A \cup B)' = A' \cap B' \quad\text{and}\quad (A \cap B)' = A' \cup B'.$$

Two sets $A$ and $B$ are disjoint if they have no elements in common, so $A \cap B = \varnothing$.

Written $\emptyset$, is the set with no elements.

A set of outcomes from a random experiment (for example, “rolling an odd number”).

Events $A$ and $B$ are independent if knowing that $A$ happened does not change the probability of $B$. Formally, $P(B\mid A)=P(B)$.

Two events are mutually exclusive if they cannot happen at the same time. In set notation, $A\cap B=\varnothing$, so $\mathrm{P}(A\cap B)=0$.

The set of all possible outcomes, often written $U$ or $S$.

A collection of objects. Each object in the set is called an element (or member) of the set.

The set of elements that are in both sets. For sets $A$ and $B$, the intersection is $A \cap B$.

A set $A$ is a subset of $B$ (written $A\subseteq B$) if every element of $A$ is also an element of $B$.

The set of elements that are in at least one of the sets. For sets $A$ and $B$, the union is $A \cup B$.

The set of all elements being considered in a given situation, usually drawn as a rectangle and often labelled $U$.