Question

★ Sets ★

1: A = { 2 , 3 , 4 , 5 } and B = { 3 , 6 , 7 , 10 } be two sets and a relation R is defined as R = $\boxed{\sf{\orange{ \{ \: ( \: x \:,\: y \: ) \: : \: x \: completely \: divides \: y \: where \: x \in A \: and \: y \in B \} }}}$ . Write the relation R in Tabular Form . Also determine $\sf{R^{-1}}$ of the relation R and also find $\sf{ d ( R^{-1} ) }$ and $\sf{ r ( R^{-1} ) }$

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Answer 1

Answer:

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)∈R

Similarly, 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}.

Answer 2

Answer:

3,6,7,10

Step-by-step explanation:

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