Question

Let $A=\left\{\right(2,5,11\left)\right\},B=\{3,6,10$} and $R$ be a relation from $A$ to $B$ defined by $R=(a,b):aandbareco-prime$. Then $R$ is

• A. $(2,3),(2,6),(5,10),(5,6)$
• B. $(2,6),(2,10),(5,10)$
• C. $(2,3),(5,3),(5,6),(11,3),(11,6),(11,10)$
• D. $(2,10),(5,3),(5,6),(11,10).$

Answer 1

The correct option is C

$(2,3),(5,3),(5,6),(11,3),(11,6),(11,10)$

Explanation for the correct option:

Option (C): $(2,3),(5,3),(5,6),(11,3),(11,6),(11,10)$

given that, $A=\left\{\right(2,5,11\left)\right\},B=\{3,6,10$} and also

$R$ be a relation from $A$ to $B$ defined by$R=\left\{(a,b):aandbareco-prime\right\}$.

co-prime are such numbers that do not have any common factor between them other than one.

So $R$ is $(2,3),(5,3),(5,6),(11,3),(11,6),(11,10)$.

Explanation for the incorrect options:

(a) In the given options $\left(2,6\right)\left(5,10\right)$ are not co-prime.

(b) In the given options none of them is a set of co-prime numbers.

(d) In the given options $\left(2,10\right)$ is not co-prime.

Therefore, option (C) is the correct option.