Question

The smallest set $A$ such that $A\cup \left\{1,2\right\}=\left\{1,2,3,5,9\right\}$ is

• A. $\left\{2,3,5\right\}$
• B. $\left\{3,5,9\right\}$
• C. $\left\{1,2,5,9\right\}$
• D. None of these

Answer 1

The correct option is B

$\left\{3,5,9\right\}$

Explanation for the correct answer:

Compute the required set:

We know,

$A\cup \left\{1,2\right\}=\left\{1,2,3,5,9\right\}$

Thus $A$will be the smallest when $A\cap \left\{1,2\right\}=\varnothing$

$\therefore$ $A=\left\{1,2,3,5,9\right\}-\left\{1,2\right\}$

$\therefore$ $A=\left\{3,5,9\right\}$

Hence, the smallest set $A$ is given as $A=\left\{3,5,9\right\}$.

Hence, option $\left(B\right)$ is the correct answer.