A relation R is defined from a set A=[2,3,4,5] to a set B=[3,6,7,10] as follows: (x,y)∈R⇔x is relatively prime to y.Express R as a set of ordered pairs and determine its domain and range.

A relation R from the set A={2,3,4,5} to B={3,6,7,10} is defined as, (x,y)∈R⇒ x is relatively prime to y.Now, it is seen that 2 is relatively prime to 3, [HCF of 2 and 3 is 1]So, (2,3)∈RSimilarly, 2 is relatively prime to 7 so that (2,7)∈R etc.So, we get R={(2,3),(2,7),(3,7),(3,10),(4,3),(4,7),(5,3),(5,6),(5,7)}Thus, domain ={2,3,4,5} and range ={3,6,7,10}.

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A relation R is defined from a set A=[2,3,4,5] to a set B=[3,6

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A relation $R$ is defined from a set $A = [2, 3, 4, 5]$ to a set $B = [3, 6, 7, 10]$ as follows:
$(x, y) \in R \Leftrightarrow x$ is relatively prime to $y$ .Express R as a set of ordered pairs and determine its domain and range.

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A relation

R

is defined from a set

A = [2, 3, 4, 5]

to a set

B = [3, 6, 7, 10]

as follows:

(x, y) \in R \Leftrightarrow x

is relatively prime to

y

.Express R as a set of ordered pairs and determine its domain and range.

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Text solutionVerified

A relation

R

from the set

A = {2, 3, 4, 5}

B = {3, 6, 7, 10}

is defined as,

(x, y) \in R \Rightarrow x

is relatively prime to

y

Now, it is seen that

2

is relatively prime to

3

, [HCF of

2

and

3

1

]

So,

(2, 3) \in R

Similarly,

2

is relatively prime to

7

so that

(2, 7) \in R

etc.

So, we get

R = {(2, 3), (2, 7), (3, 7), (3, 10), (4, 3), (4, 7), (5, 3), (5, 6), (5, 7)}

Thus, domain

= {2, 3, 4, 5}

and range

= {3, 6, 7, 10}

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Question Text	A relation $R$ is defined from a set $A = [2, 3, 4, 5]$ to a set $B = [3, 6, 7, 10]$ as follows: $(x, y) \in R \Leftrightarrow x$ is relatively prime to $y$ .Express R as a set of ordered pairs and determine its domain and range.
Answer Type	Text solution:1
Upvotes	150

A relation R is defined from a set A=[2,3,4,5] to a set B=[3,6,7,10] as follows: (x,y)∈R⇔x is relatively prime to y.Express R as a set of ordered pairs and determine its domain and range.

Text solutionVerified

Practice questions from similar books

A relation $R$ is defined from a set $A = [2, 3, 4, 5]$ to a set $B = [3, 6, 7, 10]$ as follows:
$(x, y) \in R \Leftrightarrow x$ is relatively prime to $y$ .Express R as a set of ordered pairs and determine its domain and range.