# Two questions about ordered pairs in a set

If $D= \{8,2,4,6\}$ then $(2,4) \subseteq D$. Is this true or false? From what I understand, $(2,4)$ is not the same as $\{2,4\}$ so I assume it is false?

If $B= \{5,(1,2),17\}$, then $n(B)= 4$. Does an ordered pair count as one element of a set, or two? I assume it is one and so the given statement would be false.

Anyone who can confirm/counter my suspicions would be greatly appreciated!

• Your reasoning is correct. – Strants Feb 16 '15 at 0:36

If $D=\{8,2,4,6\}$ then $(2,4)⊆D$ . Is this true or false? From what I understand, $(2,4)$ is not the same as $\{2,4\}$ so I assume it is false?

Your assumption is correct. An ordered pair is not the same as a set of two integers.

If $B=\{5,(1,2),17\}$ , then $n(B)=4$ . Does an ordered pair count as one element of a set, or two? I assume it is one and so the given statement would be false.

Again you assume correctly. An ordered pair is a single element that happens to contains two members.

You are right.

First the set $D$ contains exactly 4 elements. The interval $(2,4)$ contains infinitely many elements and so it can't be contained in $D$.

$B$ indeed does contain 3 elements:

• $5$
• $(1,2)$
• $17$.

Note that this is prefectly fine. A set can have elements of "different types".

Ordered pairs are not the same as the components themselves. An intuitive way to see this is by visualizing the x-y plane and by picturing the graph of $y=x^2$. Now, $(3,9)$ is a member of this graph, but $3$ itself is not a member of the graph, and $9$ itself is not a member of the graph.

Slightly more technically, one can define the ordered pair $(a,b)$ as $\{\{a\}, \{a,b\}\}$ and all the properties of ordered pairs work out. You can use this in reasoning about ordered pairs in the future.

In short, yes, your suspicions are spot-on. :)