Set Theory

A set is a collection of objects, called elements.
We list its elements between curly brackets.

List all possible results when rolling a standard die .

• An element is an object contained in a set.
• $\in$ means "is an element of" or "belongs to".
• $\notin$ means "is not an element of" or "does not belong to".

$2\in \{1,2,3,4,5,6\}$ and $7\notin \{1,2,3,4,5,6\}$.

Two sets are equal if they have exactly the same elements.

Determine if the sets $\{2,6,4\}$ and $\{2,4,6\}$ are equal.

Determine if the sets $\{1,2,3\}$ and $\{1,2,4\}$ are equal.

An ordered pair, denoted $(a,b)$ or $ab$, is a pair of objects in which their order is significant. The ordered pair $(a,b)$ is different from the ordered pair $(b,a)$ unless $a=b$.

In a sprint relay race, two runners are paired up. Let $L$ be Louis and $H$ be Hugo. The ordered pair $(L,H)$ means Louis runs first, then passes the baton to Hugo. The ordered pair $(H,L)$ means Hugo runs first, then passes to Louis. These are different races.

$n\left(A\right)$ denotes the number of elements in the set $A$.

$n(\{1,2,3,4,5,6\})=6=$

A universal set is the set of all elements considered.

The complement of a set $A$, denoted $A^{\prime }$, consists of all elements in $U$ that are not in $A$. Sets $A$ and $A^{\prime }$ are said to be complementary.

Given the universe $U=\{1,2,3,4,5,6\}$ and the set $A=\{1,3,5\}$, find the complement $A^{\prime }$.