Let A=&nbsp;1,2,3,4,6&nbsp;and R be the relation on A defined by “x divide y”

"Let A=1,2,3,4,6and R be the relation on A..." solved and explained

High School
Math Word Problem

Ellen Galgo

Answered question

2022-06-13

Let A= $\{1, 2, 3, 4, 6\}$ and R be the relation on A defined by “x divide y”

Answer & Explanation

madeleinejames20

Skilled2023-05-20Added 165 answers

Given:

A = {1, 2, 3, 4, 6}

and

R

is the relation on

A

defined by

x \div y

.
To find the relation

R

A

, we need to determine the ordered pairs

(x, y)

for which

x

is divisible by

y

.
Let's find all such ordered pairs:
For

x = 1

1

is divisible by

1

2

3

4

, and

6

. So, the ordered pairs for

x = 1

are

(1, 1)

(1, 2)

(1, 3)

(1, 4)

, and

(1, 6)

.
For

x = 2

2

is divisible by

1

and

2

, but not by

3

4

, or

6

. So, the ordered pairs for

x = 2

are

(2, 1)

and

(2, 2)

.
For

x = 3

3

is divisible by

1

and

3

, but not by

2

4

, or

6

. So, the ordered pairs for

x = 3

are

(3, 1)

and

(3, 3)

.
For

x = 4

4

is divisible by

1

2

, and

4

, but not by

3

6

. So, the ordered pairs for

x = 4

are

(4, 1)

(4, 2)

, and

(4, 4)

.
For

x = 6

6

is divisible by

1

2

3

, and

6

, but not by

4

. So, the ordered pairs for

x = 6

are

(6, 1)

(6, 2)

(6, 3)

, and

(6, 6)

.
Thus, the relation

R

A

defined by

x \div y

can be represented by the following set of ordered pairs:

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

.
This set represents all the pairs

(x, y)

where

x

is divisible by

y

in the given set

A

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