Question

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

• A. $\{2,3,5\}$
• B. $\{3,5,9\}$
• C. $\{1,2,5,9\}$
• D. $\{1,2\}$

Answer 1

The correct option is B $\{3,5,9\}$

Let $A$ be the smallest set.

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

$A=\{3,5,9\}$ or $\{1,2,3,5,9\}$

As $A$ is smallest set,we take $A=\{3,5,9\}$ only

Verification:-

$\{3,5,9\}\cup \{1,2\}=\{1,2,3,5,9\}$.