Write R As A Set Of Ordered Pairs

Writing relations as a set of ordered pairs may sound tricky at first, but it’s actually pretty simple once you understand how it works! Let’s dive into how to write R as a set of ordered pairs with some easy-to-understand examples, perfect for young students.

What Are The Set Of Ordered Pairs Of R?

A set of ordered pairs in relation R is just a fancy way of saying that we’re looking at two items (or numbers) that go together. For example, if you have a group of students and their favorite subjects, you could pair each student with their favorite subject. In math terms, the first item is called “x,” and the second is called “y.” Together, they form an ordered pair like (x, y).

In other words, an ordered pair is just a way of showing a relationship between two things, and that’s how we create a set of ordered pairs in relation R.

How Do You Write A Set Of Ordered Pairs?

Now, let’s get into how to write a set of ordered pairs. It’s not as hard as you think! All we do is list each pair in a certain way. The first number (x) comes from a set called the domain, and the second number (y) comes from a set called the range. For example:

If R = {(1, 2), (3, 4), (5, 6)}, this means:

The first number in each pair is from the domain.
The second number in each pair is from the range.

So, for relation R, you simply list all pairs where the first number is related to the second number. Easy, right?

What Is The Ordered Pair For R?

When we talk about the ordered pair for R, we’re really just asking about the relationship between two elements. An ordered pair in R looks like this: (x, y), where x is related to y. For example, if we say R = {(1, 3), (2, 4), (3, 5)}, then:

The ordered pair (1, 3) means that 1 is related to 3.
The ordered pair (2, 4) means that 2 is related to 4.
The ordered pair (3, 5) means that 3 is related to 5.

What Is An Example Of A Relation As A Set Of Ordered Pairs?

Let’s look at a simple example to make it clearer. If we have two sets:
A = {1, 2, 3}
B = {4, 5, 6}

And we define a relation R between these two sets as:

1 is related to 4,
2 is related to 5,
3 is related to 6.

We would write R as:

R = {(1, 4), (2, 5), (3, 6)}

This is a basic example of a relation written as a set of ordered pairs.

Write R As A Set Of Ordered Pairs For Class

If you’re working on this in class, you might be asked to write a relation like this:

Let A = {1, 3, 5}
Let B = {2, 4, 6}

Now, the relation R could be written as a set of ordered pairs like this:

R = {(1, 2), (3, 4), (5, 6)}

This is how you’d do it in class or on an assignment.

Write R As A Set Of Ordered Pairs On Brainly

Many students look for help on sites like Brainly to answer questions like this one. The steps are the same:

List your sets A and B.
Define the relationship between them.
Write each relationship as an ordered pair.

For example, if you had:

A = {1, 2, 3}
B = {4, 5, 6}
Then, you’d list the relation as:

R = {(1, 4), (2, 5), (3, 6)}

This makes it simple for anyone trying to answer the question.

Find The Domain And Range Of The Relation R

Let’s take a closer look at a specific example:
If we’re given a set A = {1, 3, 5} and a relation R = {(1, 3), (3, 5), (5, 1)}, we can figure out the domain and range of the relation.

The domain is all the first numbers in each pair. So here, the domain of R is {1, 3, 5}.
The range is all the second numbers in each pair. So the range of R is also {1, 3, 5}.

What Is The Domain Of Set A?

For another example, if set A = {1, 2, 3, 4, 5} and the relation R is defined as R = {(x, y) | x belongs to A and y belongs to A and x + 2y = 6}, we would first find which values of x and y satisfy the equation.

Let’s break it down:

If x = 1, then y = 2.5 (which doesn’t belong to set A, so skip this pair).
If x = 2, then y = 2 (which belongs to A, so the ordered pair is (2, 2)).
If x = 3, then y = 1.5 (not in set A, so skip).
If x = 4, then y = 1 (so the ordered pair is (4, 1)).

The domain of R is {2, 4} and the range is {2, 1}.

Let A = {1, 2, 3, 4}, Define A Relation R

If we’re given set A = {1, 2, 3, 4}, and the relation R is defined by the equation 3x + y = 0, where x and y belong to A, we can write the ordered pairs as:

R = {(1, -3), (2, -6), (3, -9), (4, -12)}

However, since y values like -3, -6, -9, and -12 are not part of set A, there are no valid ordered pairs for this relation.

Write AxB And Find The Number Of Relations From A To B

Given two sets A = {0, 2, 3, 4} and B = {3, 4, 5}, the Cartesian product AxB is the set of all ordered pairs (a, b) where a belongs to A and b belongs to B.

AxB = {(0, 3), (0, 4), (0, 5), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5), (4, 3), (4, 4), (4, 5)}

To find the number of possible relations from A to B, we count the number of pairs in AxB. In this case, there are 12 ordered pairs, meaning there can be 2^12 = 4096 possible relations between A and B.