Question

Please answer ASAP with explanation.

Find the relation R defined as R = {(x , x³)} where x is a prime number < 16 in roster form.

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Answer 1

$\large\underline{\sf{Given- }}$

A relation R defined as R = {(x , x³)} where x is a prime number < 16.

$\large\underline{\sf{To\:Find - }}$

Relation R = {(x , x³)} where x is a prime number < 16 in roster form

$\large\underline{\sf{Solution-}}$

Given relation is

⟼ R = {(x , x³)} where x is a prime number < 16.

⟼ So, Let first find the prime number less than 16.

We know, prime numbers are those number which are divisible by 1 or by itself.

So, prime numbers less than 16 are 2, 3, 5, 7, 11, 13

So, corresponding values are given below,

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf {x}^{3} \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 2 & \sf 8 \\ \\ \sf 3 & \sf 27\\ \\ \sf 5 & \sf 125\\ \\ \sf 7 & \sf 343\\ \\ \sf 11 & \sf 1331\\ \\ \sf 13 & \sf 2197 \end{array}} \\ \end{gathered}$

So, ordered pairs are ( 2, 8 ), ( 3, 27 ), ( 5, 125 ), ( 7, 343 ), ( 11, 1331 ) and ( 13, 2197 )

Hence,

Relation R, in roster form is

$\red{\rm :\longmapsto\:R = \{( 2, 8 ), ( 3, 27 ), ( 5, 125 ), ( 7, 343 ), ( 11, 1331 ),( 13, 2197 ) \}}$

Additional Information :-

Let R be a relation defined on set A then

1. Relation R is Reflexive if (a, a) ∈ R for all a ∈ A.

2. Relation R is symmetric if (a, b) ∈ R then (b, a) ∈ R for all a, b ∈ A.

3. Relation R is transitive if (a, b) ∈ R, (b, c) ∈ R then (a, c) ∈ R for all a, b, c ∈ A